Preoperative Pembrolizumab and Chemotherapy in Resectable, Recurrent HNSCC

Inclusion Criteria: * Participants must have histologically or cytologically confirmed locoregionally recurrent squamous cell carcinoma of the head and neck, or second primary HNSCC in a previously irradiated field, defined as \>50% of the presurgical tumor volume having prior radiation dose of \>45 Gy as determined by the treating radiation oncologist (including primary sites, such as oral cavity, oropharynx, larynx or hypopharynx carcinoma). * Participants must be a candidate for curative intent surgery. * Participants must have documented time of ≥ 6 months from completion of prior curative intent treatment for HNSCC (surgery and/or radiation therapy with/without platinum chemotherapy or cetuximab targeted therapy) to diagnosis of local or locoregional recurrence or a second primary in a previously irradiated field. * Participants must be willing to undergo a mandatory pre-treatment biopsy and willing to provide blood and tissue from the pre-treatment biopsy and at the time of surgery. Exceptions may be made after discussion with sponsor if it is not medically feasible to obtain a pre-treatment biopsy or is in the best interest of the patient. Archival tissue may be collected in this situation. Participants will be offered the opportunity to volunteer for optional biopsies at the time of recurrence of disease. * Participants may have any smoking history (no restrictions) * Participants may have any Human Papilloma Virus (HPV) status of the tumor. Patients with oropharyngeal cancer are required to undergo HPV testing with p16 immunohistochemistry and/or confirmatory HPV PCR or ISH testing * Age ≥18 years * ECOG performance status 0 or 1 (Karnofsky ≥70%, see Appendix A) * Participants must have adequate organ and marrow function as defined below: * leukocytes ≥3,000/mcL * absolute neutrophil count ≥1,500/mcL * platelets ≥100,000/mcL * total bilirubin ≤ institutional upper limit of normal (ULN) * AST(SGOT)/ALT(SGPT) ≤3 × institutional ULN * creatinine ≤ institutional ULN OR * glomerular filtration rate (GFR) ≥50 mL/min/1.73 m2 unless data exists supporting safe use at lower kidney function values, no lower than 30 mL/min/1.73 m2. * Participants with known history or current symptoms of cardiac disease, or history of treatment with cardiotoxic agents, should have a clinical risk assessment of cardiac function using the New York Heart Association Functional Classification. To be eligible for this trial, participants should be class 2B or better. * Because pembrolizumab and chemotherapy can be teratogenic, women of child-bearing potential and men must agree to use adequate contraception (hormonal or barrier method of birth control; abstinence) prior to study entry and for the duration of study participation. Should a woman become pregnant or suspect she is pregnant while she or her partner is participating in this study, she should inform her treating physician immediately. * Male participants: A male participant must agree to use a contraception as detailed in Appendix B of this protocol during the treatment period and for at least 180 days after the last dose of study treatment and refrain from donating sperm during this period. * Female participants: A female participant is eligible to participate if she is not pregnant (see Appendix B), not breastfeeding, and at least one of the following conditions applies: * a. Not a woman of childbearing potential (WOCBP) as defined in Appendix B OR * b. A WOCBP who agrees to follow the contraceptive guidance in Appendix B during the treatment period and for at least 180 days after the last dose of study treatment. * Ability to understand and the willingness to sign a written informed consent document. Exclusion Criteria: * Sinonasal, nasopharyngeal or cutaneous primary site of squamous cell carcinoma of the head and neck * Has known distant metastatic disease. Those with known brain metastases should be excluded from this clinical trial, because of the poor prognosis and because they often develop progressive neurologic dysfunction that would confound the evaluation of neurologic and other adverse events. However, baseline brain imaging is not required prior to enrollment in the study if patients are asymptomatic * Has had chemotherapy or radiotherapy for HNSCC in curative intent setting within 6 months prior to entering the study. * Has received prior therapy with an anti-PD-1, anti-PD-L1, or anti PD L2 agent or with an agent directed to another stimulatory or co-inhibitory T-cell receptor (eg, CTLA-4, OX 40, CD137). * Has received a live vaccine or live-attenuated vaccine within 30 days prior to the first dose of study drug. Administration of killed vaccines is allowed * Is currently participating in or has participated in a study of an investigational agent or has used an investigational device within 4 weeks prior to the first dose of study intervention. * Has a diagnosis of immunodeficiency or is receiving chronic systemic steroid therapy (in dosing exceeding 10 mg daily of prednisone equivalent) or any other form of immunosuppressive therapy within 7 days prior to the first dose of study drug * Has a known additional malignancy that is progressing or has required active treatment within the past 2 years. Participants with basal cell carcinoma of the skin, squamous cell carcinoma of the skin or carcinoma in situ (eg, breast carcinoma, cervical cancer in situ) that have undergone potentially curative therapy are not excluded * Has a history of allergic reactions to agents used in study * Has active autoimmune disease that has required systemic treatment in past 2 years (ie, with use of disease modifying agents, corticosteroids or immunosuppressive drugs). Replacement therapy (eg, thyroxine, insulin, or physiologic corticosteroid replacement therapy for adrenal or pituitary insufficiency) is not considered a form of systemic treatment and is allowed * Has a history of (non-infectious) pneumonitis/interstitial lung disease t