Expanding Medical Education Act of 2020 This bill permits the Health Resources and Services Administration (HRSA) to award matching grants to institutions of higher education to establish medical schools in underserved areas (i.e., areas with populations of more than 1 million and no medical schools). HRSA must prioritize awards that (1) establish medical schools in areas with fewer than 200 actively practicing physicians per 100,000 residents, and (2) emphasize care for diverse and underserved populations in the curriculum. Among other purposes, grant funds may be used for constructing facilities, hiring faculty and staff, and recruiting medical students.