Patients receive cetuximab intravenously (IV) over 120 minutes on day 1, 8, and 15 (as monotherapy for cycle 1 only) and pembrolizumab IV over 30 minutes on day 1. Treatment repeats every 3 weeks for 24 months in the absence of disease progression or unacceptable toxicity. Patients may continue pembrolizumab treatment for up to 1 year if they experience disease progression.