We present multiple ultra-high resolution cosmological hydrodynamic simulations of M 10 4−6.3 M dwarf galaxies that form within two M vir = 10 9.5−10 M dark matter halo initial conditions. Our simulations rely on the FIRE implementation of star formation feedback and were run with high enough force and mass resolution to directly resolve structure on the ∼ 200 pc scales. The resultant galaxies sit on the M vs. M vir relation required to match the Local Group stellar mass function via abundance matching. They have bursty star formation histories and also form with half-light radii and metallicities that broadly match those observed for local dwarfs at the same stellar mass. We demonstrate that it is possible to create a large (∼ 1 kpc) constant-density dark matter core in a cosmological simulation of an M 10 6.3 M dwarf galaxy within a typical M vir = 10 10 M halo -precisely the scale of interest for resolving the Too Big to Fail problem. However, these large cores are not ubiquitous and appear to correlate closely with the star formation histories of the dwarfs: dark matter cores are largest in systems that form their stars late (z 2), after the early epoch of cusp building mergers has ended. Our M 10 4 M dwarf retains a cuspy dark matter halo density profile that matches that of a dark-matter only run of the same system. Though ancient, most of the stars in our ultra-faint form after reionization; the UV field acts mainly to suppress fresh gas accretion, not to boil away gas that is already present in the proto-dwarf.