HPV-16 Vaccination and Pembrolizumab Plus Cisplatin for "Intermediate Risk" HPV-16-associated Head and Neck Squamous Cell Carcinoma

Inclusion Criteria: * Histologically-confirmed head and neck squamous cell carcinoma with no evidence of distant metastasis, with a primary site being the oropharynx. Squamous cell carcinoma of unknown primary, metastatic to cervical lymph nodes - patients can enroll provided all other eligibility criteria are met. * Patients must have intermediate risk disease. o Patients must meet one of the following criteria: Oropharynx: p16(+) PLUS HPV ISH(+) (DNA or RNA) AND one of the following; ≥ AND ≥ 10 pack-years tobacco exposure (see Tobacco Assessment Form, Appendix A) * T4 or N2c/N3 disease irrespective of tobacco exposure * Unknown primary: p16(+) PLUS HPV ISH(+) (DNA or RNA) AND one of the following * ≥ N2a AND ≥ 10 pack-years tobacco exposure * N2c/N3 disease irrespective of tobacco exposure * Patients should be considered not a candidate for curative-intent surgery with diagnosis of AJCC 7th edition Stage III, IVa, or IVb disease. * Diagnostic simple palatine or lingual tonsillectomy is permitted, provided patient has RECIST-measurable nodal disease. * Patients with a second HNSCC primary tumor are eligible for this study, provided more than 2 years have elapsed since the first diagnosis of HNSCC, the original tumor was managed with surgery only (no adjuvant chemotherapy or radiotherapy), and has not recurred. * Patients with simultaneous primaries are excluded, with the exception of patients with bilateral tonsil/base of tongue HPV+ cancers or patients with T1-2, N0, M0 differentiated thyroid carcinoma (resected or management deferred), who are eligible. * No prior systemic (chemotherapy or biologic/molecular targeted therapy) or radiation treatment for head and neck cancer. * Patients may have received chemotherapy or radiation for a previous, curatively treated non-HNSCC malignancy, provided at least 2 years have elapsed. * Patients must be untreated with radiation above the clavicles. * Patients with a history of curatively-treated non-HNSCC malignancy must be disease-free for at least 2 years except for excised and cured disease. * The patient must undergo a mandatory research biopsy at baseline. There will be 2 other optional biopsies that the patient will be asked to consent to, the first is durking week 2 of pembrolizumab/ISA101b vaccination (prior to start of cisplatin-IMRT-this correlates to week (-)1), the second once will be during week 2 after the start of IMRT (this correlates to week 1). * Eastern Cooperative Oncology Group (ECOG) Performance Status 0-1 * Age ≥ 18 * Patients must have measurable disease according to RECIST 1.1 * Patients must demonstrate adequate organ function * Written informed consent must be obtained from all patients prior to study registration. * Documentation of negative pregnancy within 10 days of treatment initiation. Exclusion Criteria: * Oral Cavity, Larynx, Hypopharynx or Nasopharyngeal primary site * Current participation in or previous participation in a study of an investigational agent or using an investigational device within 4 weeks of the first dose of study treatment. * Prior treatment with anti-HPV agents except prevention HPV vaccines * History of severe allergic or anaphylactic reactions or hypersensitivity to recombinant proteins or excipients in the investigational agents (pembrolizumab and ISA101b * Distant metastatic disease including CNS or leptomeningeal metastases is not allowed. * Acquired Immune Deficiency Syndrome (AIDS). * Received prior monoclonal antibody within 4 weeks prior to study Day 1 or who has not recovered (i.e. ≤ Grade 1 or at baseline) from adverse events due to agents administered more than 4 weeks earlier. * History of second malignancy within 2 years prior to Study Day 1 (except for excised and cured non-melanoma skin cancer, carcinoma in situ of breast or cervix, superficial bladder cancer, or T1a or T1b prostate cancer comprising \< 5% of resected tissue with normal prostate specific antigen (PSA) since resection). * Active autoimmune disease requiring systemic treatment within the past 3 months or a documented history of clinically severe autoimmune disease, or a syndrome that requires systemic steroids or immunosuppressive agents. * Acquired Immune Deficiency Syndrome (AIDS). * Known active Hepatitis B (e.g., HBsAg reactive) or Hepatitis C (e.g., HCV RNA \[qualitative\] is detected). * Received prior therapy with an anti-PD-1, anti-PD-L1, anti-PD-L2, anti-CD137, or anti-Cytotoxic T-lymphocyte-associated antigen-4 (CTLA-4) antibody (including ipilimumab or any other antibody or drug specifically targeting T-cell co-stimulation or checkpoint pathways). * Significant pulmonary disease including pulmonary hypertension, history of (non-infectious) pneumonitis that required steroids, evidence of interstitial lung disease or active, non-infectious pneumonitis * History or current evidence of any other medical or psychiatric condition, therapy, or laboratory abnormality not in the best interest of the trial or subject to participate, per the treating investigator. * Peripheral neuropathy ≥ Grade 2 * Significant cardiovascular disease. * Significant thrombotic or embolic events within 3 months prior to Study Day 1. * Major surgery within 6 weeks prior to Study Day 1 (subjects must have completely recovered from any previous surgery prior to Study Day 1). Biopsy, diagnostic tonsillectomy, airway tumor debulking or excisional lymph node biopsy do not constitute major surgery. * Active infection requiring antibiotics or antifungals within 7 days prior to first dose of study drug. * Significant electrolyte imbalance prior to enrollment (note that patients may be supplemented to achieve acceptable electrolyte values): * Pregnant or breastfeeding (due to potential for teratogenic or abortifacient effects).