  We consider a complete list of simplified models in which Majorana dark
matter particles annihilate at tree level to $hh$ or $hZ$ final states, and
calculate the loop-induced elastic scattering cross section with nuclei in each
case. Expressions for these annihilation and elastic scattering cross sections
are provided, and can be easily applied to a variety of UV complete models. We
identify several phenomenologically viable scenarios, including dark matter
that annihilates through the $s$-channel exchange of a spin-zero mediator or
through the $t$-channel exchange of a fermion. Although the elastic scattering
cross sections predicted in this class of models are generally quite small,
XENON1T and LZ should be sensitive to significant regions of this parameter
space. Models in which the dark matter annihilates to $hh$ or $hZ$ can also
generate a gamma-ray signal that is compatible with the excess observed from
the Galactic Center.
