The optical second harmonic generation (SHG) efficiency of hexagonal boron nitride (h-BN) layered materials is profoundly influenced by the symmetry properties, which has severely limited the usefulness of their SHG for nonlinear optical applications. Herein, we report on the controlled growth of large-area and continuous ultrathin h-BN films with a high density of exposed edges that show strongly enhanced SHG, owing to the breaking of inversion symmetry occurring naturally at edge sites. The large-area growth of edge-enriched BN films was accomplished through the introduction of Turing instability into a growth process that involves the liquid-gas interface self-limiting reaction between molten boron oxide (B2O3) with gaseous ammonia (NH3) at elevated temperature. Remarkably, the edge-enriched BN films give rise to a SHG response up to nearly 3 orders of magnitude higher than that of the smooth BN films prepared through the same growth approach but with different growth parameters.