Inclusion Criteria:  Recurrent/metastatic (R/M) SCCHN of the oral cavity, oropharynx, larynx and hypopharynx No prior systemic therapy for treatment of R/M disease Patients with squamous cell carcinoma of an unknown primary are eligible provided their tumor tested positive for p-16 and they have previously received treatment for locoregional head and neck cancer Must be at least four weeks since prior systemic therapy, radiation and/or surgery At least one measurable lesion as defined by Response Evaluation Criteria In Solid Tumors (RECIST) v1.1 on screening computed tomography (CT) or magnetic resonance imaging (MRI) 18 years of age and older Eastern Cooperative Oncology Group (ECOG) performance status 0-1 White blood cell (WBC) count > 2,500 cells/uL Absolute neutrophil count (ANC) >1,500 cells/uL Platelet count >= 100,000 cells/uL Hemoglobin >= 9 g/dL Creatinine =< 1.6 mg/dL Total bilirubin =< 1.6 mg/dL Serum glutamic oxaloacetic transaminase (SGOT) (aspartate transaminase [AST]), serum glutamic-pyruvic transaminase (SGPT) (alanine aminotransferase [ALT]) =< 2.5 x upper limit of normal (ULN) Potassium >= lower limit of normal (LLN) Willingness to use medically acceptable contraception throughout the study period and four weeks after the final administration of treatment For female subjects with reproductive potential: a negative serum pregnancy test at baseline Ability and willingness to provide written informed consent and to comply with the study visits and assessment schedule  Exclusion Criteria:  Disease which is amenable to curative local therapy Nasopharyngeal, salivary gland, lip, or sinonasal carcinoma Disease that requires corticosteroids (>10 mg prednisone or equivalent daily within four weeks prior to the first dose of cemiplimab) or other immune suppressives at baseline Previous treatment with mAb-based immune therapies Previous treatment with PI3K inhibitors Known brain metastases, unless stable for at least 21 days prior to registration Known infection human immunodeficiency virus (HIV), hepatitis B or C Clinically significant cardiac disease (e.g., congestive heart failure, unstable or uncontrolled angina, myocardial infarction) within the past six months History of pneumonitis within the past five years Recipient of live vaccines (including attenuated) within 30 days of study treatment Female patients who are pregnant or breast-feeding Any other condition or circumstance that could interfere with adherence to the study's procedures or requirements or otherwise compromise the study's objectives in the opinion of the Principal Investigator