  We study two-dimensional charge-imbalanced electron-hole systems embedded in
an optical microcavity. We find that strong coupling to photons favors states
with pairing at zero or small center of mass momentum, leading to a condensed
state with spontaneously broken time-reversal and rotational symmetry, and
unpaired carriers that occupy an anisotropic crescent-shaped sliver of momentum
space. The crescent state is favoured at moderate charge imbalance, while a
Fulde--Ferrel--Larkin--Ovchinnikov-like state --- with pairing at large center
of mass momentum --- occurs instead at strong imbalance. The crescent state
stability results from long-range Coulomb interactions in combination with
extremely long-range photon-mediated interactions.
