Immigration Visa Efficiency and Security Act of 2023 This bill addresses issues concerning family- and employment-based visas. The bill increases the annual per-country cap on family-based immigrant visas from 7% of the total number of such visas available to 15% and eliminates the per-country cap for employment-based immigrant visas. The bill establishes transition rules for employment-based visas such as (1) reserving a percentage of EB-2 (workers with advanced degrees or exceptional ability) and EB-3 (skilled and other workers) visas for individuals not from the two countries with the largest number of recipients of such visas, and (2) allotting a number of visas for professional nurses and physical therapists. The bill imposes additional requirements for H-1B visas, such as prohibiting (1) an employer from advertising that a position is limited to H-1B applicants or that H-1B applicants are preferred, and (2) certain employers from having more than half of their employees as nonimmigrant visa workers. The Department of Labor shall create a publicly available website where an employer seeking an H-1B visa must post information about the open position. The bill also expands Labor's authority to investigate H-1B applications for fraud or misrepresentations. The bill also prohibits H-1B or H-3 (trainee or special education exchange) visas for nationals of a foreign adversary country for employment in any matter vital to U.S. national interests. The bill also allows certain nonimmigrant visa holders to obtain lawful permanent resident status if the individual (1) has an approved immigrant visa petition, and (2) has waited at least two years for a visa.