Expanding Nutrition's Role in Curricula and Healthcare Act or the ENRICH Act This bill requires the Health Resources and Services Administration to establish a program of three-year competitive grants to accredited medical schools for the development or expansion of an integrated nutrition and physical-activity curriculum. The curriculum must (1) be designed to improve communication and provider preparedness in the prevention, management, and reversal of obesity, cardiovascular disease, diabetes, and cancer; and (2) address additional topics regarding individuals in at-risk populations, as practicable, including physical-activity and training programs, food insecurity, and malnutrition.