  Two dimensional materials and their heterostructures constitute a promising
platform to study correlated electronic states as well as many body physics of
excitons. Here, we present experiments that unite these hitherto separate
efforts and show how excitons that are dynamically screened by itinerant
electrons to form exciton-polarons, can be used as a spectroscopic tool to
study interaction-induced incompressible states of electrons. The
MoSe$_2$/hBN/MoSe$_2$ heterostructure that we study exhibits a long-period
Moir\'e superlattice as evidenced by coherent-hole tunneling mediated avoided
crossings between the intra-layer exciton with three inter-layer exciton
resonances separated by $\sim$ 3meV. For electron densities corresponding to
half-filling of the lowest Moir\'e subband, we observe strong
layer-paramagnetism demonstrated by an abrupt transfer of all $\sim$ 1500
electrons from one MoSe$_2$ layer to the other upon application of a small
perpendicular electric field. Remarkably, the electronic state at half-filling
of each MoSe$_2$ layer is resilient towards charge redistribution by the
applied electric field, demonstrating an incompressible Mott-like state of
electrons. Our experiments demonstrate that optical spectroscopy provides a
powerful tool for investigating strongly correlated electron physics in the
bulk and pave the way for investigating Bose-Fermi mixtures of degenerate
electrons and dipolar excitons.
