Cemiplimab and Quad Shot Radiation for Cutaneous Squamous Cell Carcinoma in the Head and Neck

Inclusion Criteria: 1. Locally advanced squamous cell carcinoma of the skin arising from the head and neck region. 2. Patients who have had prior treatment of a localized skin primary and now present with nodal recurrence or unresectable local recurrence are considered eligible as long as the recurrent disease has not been previously treated with radiation therapy 3. No prior systemic therapy including chemotherapy, targeted therapy or immunotherapy. 4. Deemed unfit for definitive curative intent treatment with surgery or radiation therapy due to one of the following criteria: * ECOG Performance status 3 or 4; * significant co-morbid medical conditions. * frailty due to advanced age (must be \> 70 years of age if using this criterion only). 5. At least one measurable lesion as defined by RECIST 1.1. 6. Tumor tissue available for correlative-sequencing (tumor tissue from bony metastasis is not suitable; however, archival tissue is acceptable). A minimum of 6 cores from initial lymph node biopsy is strongly encouraged. 7. Adequate organ function as defined by: • Absolute neutrophil count \>= 1,000/ul * Platelets \>= 75,000/ul * Hemoglobin \>= 7 g/dL (without requirement for transfusion in prior 4 weeks) * Calculated serum creatinine clearance \> 20 mL/min by the Cockcroft-Gault formula (clearance \< 20mL/min will be allowed if patient is on a stable dialysis regimen) * Total bilirubin =\< 1.5 X upper normal limit (UNL) (except subjects with Gilbert syndrome, who can have total bilirubin \< 3 mg/dl) * Aspartate aminotransferase (AST) =\< 3.0 X UNL * Alanine aminotransferase (ALT) =\< 3.0 X UN 8. Willing and able to sign informed consent. 9. Male or female ≥ 18 years of age at the time of informed consent. 10. Women of childbearing potential (WOCBP) must have a negative serum pregnancy test during screening and prior to receiving first dose of protocol-indicated treatment. * Women of childbearing potential (WOCBP) is defined as any female who has experienced menarche who has not undergone surgical sterilization (hysterectomy or bilateral oophorectomy) or is not postmenopausal. * Menopause is defined clinically as 12 months of amenorrhea in a woman over 45 years of age in the absence of other biological or physiological causes. * Women of childbearing potential must agree to use of contraceptives to prevent pregnancy. Exclusion Criteria: 1. Prior systemic therapy for locally advanced cutaneous carcinoma of the head and neck (LACCHN) 2. Metastatic disease outside of the head and neck. 3. Prior treatment with checkpoint inhibitor therapy. 4. Planned re-irradiation: If disease is recurrent in a site previously treated with radiation, the patient will not be considered for study. 5. Active wound and/or infection overlaying the head or neck region that would prohibit safe radiation delivery. 6. Active second malignancy. Second malignancies that have been either cured or definitively treated and in remission are acceptable for inclusion. 7. Presence of cardiovascular disease, as defined by either: \- New York Heart Association heart failure classifications of Class II, III, or IV; or myocardial infarction, or acute coronary syndrome within 12 months of first dose of study medication. \- Transient ischemic attack or stroke within 1 year 8. Exclusions relating to infection or immunodeficiency including: \- Any condition that requires ongoing/continuous corticosteroid therapy (\>10 mg prednisone/day or anti-inflammatory equivalent) within 1 week prior to the first dose of study medication. Participants who require a brief course of steroids (up to 2 days in the week before enrollment) or physiologic replacement are not excluded. \- Ongoing or recent evidence of significant autoimmune disease that required treatment with systemic immunosuppressive treatments. Note: The following are not exclusionary: vitiligo, childhood asthma that has resolved, endocrinopathies (such as hypothyroidism or type 1 diabetes) that require only hormone replacement, or psoriasis that does not require systemic treatment. \- Any infection requiring hospitalization or treatment with IV anti- infectives within 2 weeks of first dose of study medication \- Uncontrolled infection with HIV, hepatitis B or hepatitis C infection, diagnosis of immunodeficiency, and/or tuberculosis (active or latent). Participants with known controlled HIV infection (undetectable viral load on HIV RNA PCR) and CD4 count above 350 either spontaneously or on a stable antiviral regimen are eligible. For these participants monitoring will be performed per local standards. \- Prior recipient of organ transplantation. 9. Exclusions relating to vaccines including: * Receipt of a live vaccine within 4 weeks of start of study medication * Receipt of COVID-19 vaccination within 1 week of planned start of study medication or for which the planned COVID-19 vaccinations would not be completed 1 week prior to start of study medication. Exclusions relating to hypersensitivity including: * Known hypersensitivity to the active substances or to any of the excipients. Exclusions and information relating to pregnancy/contraception: \- WOCBP\* and men\*\* who are unwilling to practice highly effective contraception prior to the initial dose/start of the first treatment, during the study, and for at least 6 months after the last dose. Highly effective contraceptive measures include: 1. Stable use of combined (estrogen and progestogen containing) hormonal contraception (oral, intravaginal, transdermal) or progestogen-only hormonal contraception (oral, injectable, implantable) associated with inhibition of ovulation initiated 2 or more menstrual cycles prior to screening; 2. Intrauterine device; intrauterine hormone-releasing system; 3. Bilateral tubal occlusion/ligation; 4. Vasectomized partner (provided that the male vasectomized partner is the sole sexual partner of the WOCBP study participant and that the vasectomized partner has obtained medical assessment of surgical success for the procedure); and/or 5. Sexual abstinence Pregnancy testing and contraception are required for WOCBP. Pregnancy testing and contraception are not required for women who are postmenopausal or permanently sterile. * WOCBP are defined as women who are fertile following menarche until becoming postmenopausal, unless permanently sterile. Permanent sterilization methods include hysterectomy, bilateral salpingectomy, and bilateral oophorectomy. A postmenopausal state is defined as no menses for 12 months without an alternative medical cause. A high FSH level in the postmenopausal range may be used to confirm a postmenopausal state in women not using hormonal contraception or hormonal replacement therapy. However, in the absence of 12 months of amenorrhea, a single FSH measurement is insufficient to determine the occurrence of a postmenopausal state. The above definitions are according to the CTFG guidance. Pregnancy testing and contraception are not required for women with documents hysterectomy or tubal ligation. \*\*Male participants: A male participant will be excluded from the study if that participant does not agree to use condoms or practice sexual abstinence†‡, unless vasectomized, prior to the initial dose/start of study medication, during the study, and for at least 6 months after the last dose. Sperm donation is also prohibited during the same period. Vasectomy success must be confirmed by semen analysis. Prohibited medications Participants must not receive live vaccines during the study. Participants using immunosuppressive doses (≥10 mg per day of prednisone or equivalent) of systemic corticosteroids other than for physiologic corticosteroid replacement are not eligible for the study. Participants should not receive systemic corticosteroids such as hydrocortisone, prednisone, prednisolone (Solu-Medrol®) or dexamethasone (Decadron®) at any time throughout the study except as required premedication for chemotherapy or another study treatment per protocol and in the case of a life-threatening emergency and/or to treat an imAE. Similarly, it is recommended that participants do not receive other immunosuppressive medications (eg, methotrexate) at any time throughout the study except in the case of a life-threatening emergency and/or to treat an imAE. Other immunosuppressive medications required to treat imAEs, IRRs, or life-threatening emergencies may be used at the investigator's discretion. Investigators are allowed to treat TEAEs requiring immunosuppressive medication per standard of care which may involve medications not specifically mentioned in the protocol.