We demonstrate for the first time an entirely molecular beam epitaxy (MBE) approach to high-quality GaAs planar coalescence over embedded dielectric microstructures. Specifically, an all-MBE approach was achieved by developing a new two-stage growth process, merging the MBE growth regimes of III-flux modulated lateral epitaxial overgrowth (LEO) with self-ordered planarization of nonplanar substrates to produce highly selective planar coalescence specifically for embedding [010]-aligned silica gratings patterned on (001) substrates. The resulting planar coalescence returned a smooth (001) surface with surface roughness as low as 3 nm root-mean-square and photoluminescence (PL) equivalent to grating-free controls. In demonstrating high-quality GaAs coalescence, we also report for the first time an intentionally enhanced single InGaAs/GaAs/AlAs quantum well PL test structure seamlessly grown directly above embedded silica gratings, leading to a 1.4× enhancement in PL as a result of both Purcell and extraction enhancements corroborated by time-resolved PL studies. As a result, we provide a significant advance to the long-standing challenge of marrying high-quality semiconductor crystal growth with dielectric microstructures, unlocking several high-impact applications, such as enhanced quantum emitters and embedded metasurfaces for quantum information processing, and provide a pathway for all-MBE metamorphic III−V heteroepitaxy.