Exhibit 1.1

[Letterhead of Sandler O’Neill & Partners, L.P.]

August 17, 2016

PCSB Bank

2651 Strang Boulevard

Suite 100

Yorktown Heights, NY 10598

Ladies and Gentlemen:

We understand that the Board of Trustees of PCSB Bank (the “Bank”) is considering the adoption of a Plan of Conversion (the “Plan”) pursuant to which the Bank will be converted into stock form and shares of the common stock (the “Shares”) of a newly organized stock holding company (the “Holding Company”) for the Bank will be offered and sold in a public offering. The Holding Company and the Bank are sometimes collectively referred to herein as the “Company.” Sandler O’Neill & Partners, L.P. (“Sandler O’Neill”) is pleased to assist the Company with the Offering and this letter is to confirm the terms and conditions of our engagement.

Under the terms of the Plan and applicable regulations, the Shares will be offered first to eligible depositors of the Bank and the Company’s tax-qualified employee stock benefit plans in a subscription offering (the “Subscription Offering”). Subject to the prior rights of subscribers in the subscription offering, the Shares may be offered in a community offering, with a preference given in the community offering to residents of the communities served by the Bank (the “Community Offering,” and together with the Subscription Offering, the “Subscription and Community Offering”). Shares not subscribed for in the Subscription and Community Offering, if any, may be offered to the general public by Sandler O’Neill on a best efforts basis (a “Syndicated Offering”) or in a firm commitment offering (a “Firm Commitment Offering,” and together with the Subscription and Community Offering and any Syndicated Offering, the “Offering”).

OFFERING SERVICES

Sandler O’Neill will work with the Company and its management, counsel, accountants and other advisors in preparing for and completing the Offering and anticipate that our services will include the following:

1. Consulting as to the financial and marketing implications of the Plan;

Board of Trustees

PCSB Bank

August 17, 2016

Page 2

2. Reviewing with the Board the financial impact of the Offering on the Company, based upon the independent appraiser’s appraisal of the Holding Company’s common stock;

3. Reviewing all offering documents, including the Prospectus, stock order forms and related offering materials (it being understood that preparation and filing of such documents will be the responsibility of the Company and its counsel);

4. Assisting in the design and implementation of a marketing strategy for the Offering;

5. Assisting the Company’s management in scheduling and preparing for meetings with potential investors and/or other broker/dealers in connection with the Offering; and

6. Providing such other general advice and assistance as may be reasonably necessary to promote the successful completion of the Offering.

Sandler O’Neill will act as exclusive marketing agent for the Company in the Subscription and Community Offering and will serve as sole book-running manager of the Syndicated Offering and/or Firm Commitment Offering. It is understood that neither Sandler O’Neill nor any other broker/dealer shall be obligated to take or purchase any Shares in the Offering other than as may be expressly agreed to by such firms and the Company in an underwriting agreement for a Firm Commitment Offering.

FEES

If the Offering is consummated, the Company agrees to pay Sandler O’Neill for its marketing agent services a fee of ninety basis points (0.90%) of the aggregate Actual Purchase Price of all Shares sold in the Subscription and Community Offering, excluding Shares purchased by or on behalf of (i) any employee benefit plan or trust of the Company established for the benefit of its trustees, directors, officers and employees, and (ii) any director, trustee, officer or employee of the Company or members of their immediate families (whether directly, as a participant in an employee plan or through a business, trust or other entity controlled by such person or as to which such person is the primary beneficiary), as to which no fee shall be payable. For the avoidance of doubt, no fee shall be charged in connection with any shares issued to the Company’s charitable foundation established in connection with the conversion.

With respect to any Shares sold in a Syndicated Offering and/or Firm Commitment Offering, the Company agrees to pay Sandler O’Neill and any other participating broker/dealers an aggregate fee of 5.0% of the aggregate Actual Purchase Price of all Shares sold in the Syndicated Offering and/or Firm Commitment Offering.

Board of Trustees

PCSB Bank

August 17, 2016

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For purposes of this letter, the term “Actual Purchase Price” shall mean the price at which the Shares are sold in the Offering and the term “immediate family” shall mean a spouse and any children living in the same household as the director, trustee, officer or employee. All fees payable hereunder shall be due and payable in immediately available funds by wire transfer at the time of the closing of the Offering. If (a) Sandler O’Neill’s engagement hereunder is terminated for any of the reasons provided for under the second paragraph of the section of this letter captioned “Definitive Agreement,” or (b) the Offering is terminated by the Company, no fees shall be payable by the Company to Sandler O’Neill hereunder.

COSTS AND EXPENSES

In addition to any fees that may be payable to Sandler O’Neill hereunder and the expenses to be borne by the Company pursuant to the following paragraph, the Company agrees to reimburse Sandler O’Neill, upon request made from time to time, for its reasonable out-of-pocket expenses incurred in connection with its engagement hereunder, regardless of whether the Offering is consummated, including, without limitation, legal fees and expenses incurred in connection with its engagement hereunder, regardless of whether the Offering is consummated, up to a maximum of $110,000, which expense cap shall be increased to $125,000 if a Syndicated Offering or Firm Commitment Offering is undertaken; provided, however, that Sandler O’Neill shall document such expenses to the reasonable satisfaction of the Company. The provisions of this paragraph are not intended to apply to or in any way impair the indemnification provisions of this letter.

As is customary, the Company will bear all other expenses incurred in connection with the Offering, including, without limitation, (i) the cost of obtaining all securities and bank regulatory approvals, including any required FINRA filing fees; (ii) the cost of printing and distributing the offering materials; (iii) the costs of blue sky qualification (including fees and expenses of blue sky counsel) of the Shares in the various states; (iv) listing fees; and (v) all fees and disbursements of the Company’s counsel, accountants, transfer agent and other advisors; and (vi) the establishment and operational expenses for the Conversion Center (e.g., postage, telephones, supplies, temporary employees, etc.). In the event Sandler O’Neill incurs any such fees and expenses on behalf of the Company, the Company will reimburse Sandler O’Neill for such fees and expenses whether or not the Offering is consummated.

Board of Trustees

PCSB Bank

August 17, 2016

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DUE DILIGENCE REVIEW

Sandler O’Neill’s obligation to perform the services contemplated by this letter shall be subject to the satisfactory completion of such investigation and inquiries relating to the Company and its trustees, directors, officers, agents and employees as Sandler O’Neill and its counsel in their sole discretion may deem appropriate under the circumstances. In this regard, the Company agrees that, at its expense, it will make available to Sandler O’Neill all information that Sandler O’Neill requests, and will allow Sandler O’Neill the opportunity to discuss with the Company’s management the financial condition, business and operations of the Company. The Company acknowledges that Sandler O’Neill will rely upon the accuracy and completeness of all information received from the Company and its trustees, directors, officers, employees, agents, independent accountants and counsel.

BLUE SKY MATTERS

Sandler O’Neill and the Company agree that the Company’s counsel shall serve as counsel with respect to blue sky matters in connection with the Offering. The Company will cause such counsel to prepare a Blue Sky Memorandum related to the Offering, including Sandler O’Neill’s and any other broker-dealer’s participation therein, and shall furnish Sandler O’Neill a copy thereof addressed to Sandler O’Neill or upon which such counsel shall state Sandler O’Neill may rely.

CONFIDENTIALITY

Except as contemplated in connection with the performance of its services under this agreement, as authorized by the Company or as required by law, regulation or legal process, Sandler O’Neill agrees that it will treat as confidential all material, non-public information relating to the Company obtained in connection with its engagement hereunder (the “Confidential Information”); provided, however, that Sandler O’Neill may disclose such information to its agents and advisors who are assisting or advising Sandler O’Neill in performing its services hereunder and who have been directed to comply with the confidentiality terms and conditions of this paragraph. As used in this paragraph, the term “Confidential Information” shall not include information which (a) is or becomes generally available to the public other than as a result of a disclosure by Sandler O’Neill in breach of the confidentiality provisions contained herein, (b) was available to Sandler O’Neill on a non-confidential basis prior to its disclosure to Sandler O’Neill by the Company, (c) becomes available to Sandler O’Neill on a non-confidential basis from a person other than the Company who is not known by Sandler O’Neill to be bound not to disclose such information pursuant to a contractual, legal or fiduciary obligation owed to the Company, or (d) is independently developed by Sandler O’Neill without use of or reference to the Confidential Information disclosed hereunder.

The Company hereby acknowledges and agrees that the financial models and presentations used by Sandler O’Neill in performing its services hereunder have been developed by and are proprietary to Sandler O’Neill and are protected under applicable copyright laws. The Company agrees that it will not reproduce or distribute all or any portion of such models or presentations without the prior written consent of Sandler O’Neill.

Board of Trustees

PCSB Bank

August 17, 2016

Page 5

INDEMNIFICATION

Since Sandler O’Neill will be acting on behalf of the Company in connection with the Offering, each of the Bank and the Holding Company agrees to indemnify and hold Sandler O’Neill, its affiliates and their respective partners, directors, officers, employees, agents and controlling persons within the meaning of Section 15 of the Securities Act of 1933 or Section 20 of the Securities Exchange Act of 1934 (Sandler O’Neill and each such person being an “Indemnified Party”) harmless from and against any and all losses, claims, damages and liabilities, joint or several, to which such Indemnified Party may become subject under applicable federal or state law, or otherwise, related to or arising out of the Offering or the engagement of Sandler O’Neill pursuant to, or the performance by Sandler O’Neill of the services contemplated by, this letter, and will reimburse any Indemnified Party for all expenses (including reasonable legal fees and expenses) as they are incurred, including expenses incurred in connection with the investigation of, preparation for or defense of any pending or threatened claim or any action or proceeding arising therefrom, whether or not such Indemnified Party is a party; provided, however, that the Company will not be liable in any such case to the extent that any such loss, claim, damage, liability or expense (i) arises out of or is based upon any untrue statement of a material fact or the omission of a material fact required to be stated therein or necessary to make not misleading any statements contained in any final prospectus, or any amendment or supplement thereto, made in reliance on and in conformity with written information furnished to the Company by Sandler O’Neill expressly for use therein, or (ii) is primarily attributable to the gross negligence, willful misconduct or bad faith of Sandler O’Neill. If the foregoing indemnification is unavailable for any reason, the Company agrees to contribute to such losses, claims, damages, liabilities and expenses in the proportion that its financial interest in the Offering bears to that of Sandler O’Neill.

The Company agrees to notify Sandler O’Neill promptly of the assertion against it or any other person of any claim or the commencement of any action or proceeding relating to any transaction contemplated by this agreement.

DEFINITIVE AGREEMENT

Sandler O’Neill and the Company agree that (a) except as set forth in clause (b) below, the foregoing represents the general intention of the Company and Sandler O’Neill with respect to the services to be provided by Sandler O’Neill in connection with the Offering, which will serve as a basis for Sandler O’Neill commencing activities, and (b) the only legal and binding obligations of the Company and Sandler O’Neill with respect to the Offering shall be (1) the Company’s obligation to

Board of Trustees

PCSB Bank

August 17, 2016

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reimburse costs and expenses pursuant to the section captioned “Costs and Expenses,” (2) those set forth under the captions “Confidentiality” and “Indemnification,” and (3) as set forth in a duly negotiated and executed definitive Agency Agreement to be entered into prior to the commencement of the Subscription Offering, and a duly negotiated and executed Underwriting Agreement to be entered into prior to the commencement of any Firm Commitment Offering. Such Agency Agreement and Underwriting Agreement shall be in form and content satisfactory to Sandler O’Neill and the Company and their respective counsel and shall contain standard indemnification and contribution provisions consistent herewith.

Sandler O’Neill’s execution of such Agency Agreement and Underwriting Agreement shall also be subject to (i) Sandler O’Neill’s satisfaction with its investigation of the Company’s business, financial condition and results of operations, (ii) preparation of offering materials that are satisfactory to Sandler O’Neill and its counsel, (iii) compliance with all relevant legal and regulatory requirements to the reasonable satisfaction of Sandler O’Neill and its counsel, (iv) agreement that the price established by the independent appraiser is reasonable, and (v) market conditions at the time of the proposed offering. Sandler O’Neill may terminate this agreement if such Agency Agreement is not entered into prior to June 30, 2017.

REPRESENTATIONS

The Company represents and warrants that it has all requisite power and authority to enter into and carry out the terms and provisions of this agreement, the execution, delivery and performance of this agreement does not breach or conflict with any agreement, document or instrument to which it is a party or bound and this agreement has been duly authorized, executed and delivered by the Company.

MISCELLANEOUS

This Agreement constitutes the entire agreement between the parties with respect to the subject matter hereof and can be altered only by written consent signed by the parties. This Agreement shall be construed and enforced in accordance with the laws of the State of New York, without regard to the conflicts of laws principles thereof.

Board of Trustees

PCSB Bank

August 17, 2016

Page 7

Please confirm that the foregoing correctly sets forth our agreement by signing and returning to Sandler O’Neill the duplicate copy of this letter enclosed herewith.