We report on the development of a new technique for the growth of graphene and graphite nanocrystals from a metal-carbon melt. The process involves dissolving carbon inside molten nickel or copper at a specified temperature and then allowing the dissolved carbon to nucleate and grow on top of the melt at a lower temperature. The morphology of graphite forming inside nickel is shown to depend on the melt composition and cooling rate. The results indicate that the graphene layers contain a wrinkled structure due to thermal expansion coefficient mismatch between the grown layers and substrate. The graphene layers, however, preserve their continuity over these wrinkles. Although the formation of wrinkles was found not to depend on the type of metal substrate, the substrate had strong effect on the quality of grown layers. The films on copper contained quite a few defects including cracks and entrapped vacancies, whereas the films grown on nickel were pristine and defects free.