Protecting Americans from Unsafe Drugs Act of 2023 This bill expands the authority of the Secretary of the Department of Health and Human Services (HHS) to order the recall of controlled substances to cover all drugs. Furthermore, the authority to issue such an order may be delegated to the Director of the Center for Drug Evaluation and Research or the Director of the Center for Biologics Evaluation and Research (or an official senior to either director), whereas currently this authority may only be delegated to the Director of the Center for Drug Evaluation and Research or an official senior to such director. (Both centers are located in the Food and Drug Administration within HHS.)