The purpose of this study is to find out if the combination of two established anti-cancer therapies are beneficial in participants with Head and Neck Squamous Cell Carcinoma (HNSCC). Specifically, investigators want to determine if the combination of Cetuximab and nivolumab can help people with advanced cases of HNSCC. Both cetuximab and nivolumab have been used separately to treat HNSCC and are Food and Drug Administration (FDA) approved in this type of cancer.