  We derive the splitting kernels for partons produced in large $Q^2$
scattering processes that subsequently traverse a region of
strongly-interacting matter using a recently-developed effective theory \SCETG.
We include all corrections beyond the small-$x$ approximation, consistent with
the power counting of \SCETG. We demonstrate how medium recoil, geometry and
expansion scenarios, and phase space cuts can be implemented numerically for
phenomenological applications. For the simplified case of infinite transverse
momentum kinematics and a uniform medium, we provide closed-form analytic
results that can be used to validate the numerical simulations.
