Primordial black holes (PBHs) are a viable candidate for dark matter if the PBH masses are in the currently unconstrained "sublunar" mass range. We revisit the possibility that PBHs were produced by nucleation of false vacuum bubbles during inflation. We show that this scenario can produce a population of PBHs that simultaneously accounts for all dark matter, explains the candidate event in the Subaru Hyper Suprime-Cam (HSC) data, and contains both heavy black holes as observed by LIGO and very heavy seeds of supermassive black holes. We demonstrate with numerical studies that future observations of HSC, as well as other optical surveys, such as LSST, will be able to provide a definitive test for this generic PBH formation mechanism if it is the dominant source of dark matter.