This is a prospective, open-label, non-randomized, two-cohort, single-arm Phase 2 study in adults with unresectable or recurrent/metastatic head and neck squamous cell carcinoma, excluding nasopharyngeal carcinoma. The study will evaluate the efficacy and safety of Becotatug vedotin, an EGFR-targeted antibody-drug conjugate, in combination with an investigator-selected PD-1 inhibitor. Participants will enter one of two cohorts based on prior treatment: those who have not received prior systemic treatment for unresectable or recurrent/metastatic disease, and those who have received at least one prior line of treatment. Becotatug vedotin will be given once every 21 days with the PD-1 inhibitor. Treatment may continue until disease progression, unacceptable side effects, withdrawal of consent, death, or other protocol-defined reasons. The main purpose is to assess objective response rate, defined as the percentage of participants whose tumors have a complete or partial response. Other outcomes include safety, tolerability, progression-free survival, overall survival, disease control rate, and duration of response.