Building a Health Care Workforce for the Future Act This bill establishes, within the Department of Health and Human Services (HHS), grant programs for health professional education and training. It also requires the National Academy of Medicine (formerly known as the Institute of Medicine) to study the documentation requirements for cognitive services under Medicare, Medicaid, and private health insurers, including administrative and labor costs of such documentation. For the first grant program, HHS must award matching grants to states for scholarships to ensure an adequate supply of health professionals. As a condition of receiving scholarships, recipients must agree to work in areas with shortages of health care providers for one year for each year they receive the scholarship. For the second grant program, HHS must award grants to medical and other health professions schools to improve curricula for, and education and training on, certain priority competencies, such as patient-centered medical homes and chronic disease management. The Advisory Committee on Training in Primary Care Medicine and Dentistry shall select these competencies annually. For the last grant program, HHS may award grants to medical schools for primary care mentorship programs to support faculty who serve as mentors and encourage interest in primary care among students.