  A statistically significant excess of gamma rays has been reported and
robustly confirmed in the Galactic Center over the past decade. Large local
dark matter densities suggest that this Galactic Center Excess (GCE) may be
attributable to new physics, and indeed it has been shown that this signal is
well-modelled by annihilations dominantly into $b\bar{b}$ with a WIMP-scale
cross section. In this paper, we consider Majorana dark matter annihilating
through a Higgs portal as a candidate source for this signal, where a large
CP-violation in the Higgs coupling may serve to severely suppress scattering
rates. In particular, we explore the phenomenology of two minimal UV
completions, a singlet-doublet model and a doublet-triplet model, and map out
the available parameter space which can give a viable signal while respecting
current experimental constraints.
