  We develop a theory for a continuous bandwidth-tuned transition at fixed
\textit{fractional} electron filling from a metal with a generic Fermi surface
to a `Wigner-Mott' insulator that spontaneously breaks crystalline space-group
symmetries. Across the quantum critical point, (i) the entire electronic Fermi
surface disappears abruptly upon approaching from the metallic side, and (ii)
the insulating charge gap and various order parameters associated with the
spontaneously broken space-group symmetries vanish continuously upon
approaching from the insulating side. Additionally, the insulating side hosts a
Fermi surface of neutral spinons. We present a framework for describing such
continuous metal-insulator transitions (MITs) and analyze the example of a
bandwidth-tuned transition at a filling, $\nu=1/6$, for spinful electrons on
the triangular lattice. By extending the theory to a certain large-$N$ limit,
we provide a concrete example of such a continuous MIT and discuss numerous
experimental signatures near the critical point. We place our results in the
context of recent experiments in moir\'e transition metal dichalcogenide
materials.
