This study will be a first-in-human (FIH), Phase 1, multicenter, open-label study to determine the safety, tolerability, PK, PD, and preliminary anti-tumor activity of ascending doses of EPI-326 as a single agent administered to patients with EGFR-mutant (per clinically validated molecular testing, e.g., next-generation sequencing \[NGS\]) locally advanced or metastatic NSCLC and locally advanced or metastatic HNSCC. All patients will be treated until documented disease progression, unacceptable toxicity, withdrawal of consent, or study termination.