We compute the differential cross-section for inclusive prompt photon production in deeply inelastic electron-nucleus scattering at small $x$ in the framework of the Color Glass Condensate (CGC) effective field theory (EFT). At leading order in $\alpha_s$, but all orders in $Q_s^2/Q^2$, where $Q_s$ is the saturation scale in the nucleus, our result is proportional to universal dipole and quadrupole Wilson line correlators in the nucleus. Leading twist $k_{\perp}$ and collinearly factorized results are recovered in appropriate limits. We outline recent progress in extending the LO results to NLO+NLL$x$ accuracy.