Expanding Health Care Providers for Veterans Act This bill exempts certain workers involved with providing care for veterans from the annual cap on H-1B visas (specialty occupations). Specifically, an H-1B visa shall not count against the annual cap if the visa holder is employed (or has received a job offer) at the Department of Veterans Affairs or a State home (generally, a facility established by a state or Indian tribe for disabled veterans). (The annual H-1B cap is 65,000 visas with various exemptions and additional visas available to certain categories of workers.)