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Hexagonal boron nitride encapsulation is the method of choice for protecting graphene from environmental doping and impurity scattering. It was previously demonstrated that metal–organic vapor phase epitaxy (MOVPE) grows epitaxially ordered, uniform BN layers on epigraphene (graphene grown on SiC). Due to graphene’s nonwetting properties, h-BN growth starts preferentially from the graphene ledges. We use this fact here to selectively promote the growth of high-quality flat h-BN on epigraphene by patterning epigraphene microstructures prior to BN growth. Thin h-BN films (down to 6 nm) grown by MOVPE show a smooth and pleated surface morphology on epigraphene, whereas crumpled BN is observed on the SiC. Cross-sectional high-resolution transmission electron microscopy images and fluorescence imaging confirm the higher BN quality grown on the epigraphene. Transport measurements reveal p-doping, as expected from hydrogen intercalation of epigraphene and regions of high and low mobility. This method can be used to produce structurally uniform high-quality h-BN/epigraphene micro/nanoscale heterostructures.