  We derive medium-induced splitting kernels for energetic partons that undergo
interactions in dense QCD matter before a hard-scattering event at large
momentum transfer $Q^2$. Working in the framework of the effective theory ${\rm
SCET}_{\rm G}\,$, we compute the splitting kernels beyond the soft gluon
approximation. We present numerical studies that compare our new results with
previous findings. We expect the full medium-induced splitting kernels to be
most relevant for the extension of initial-state cold nuclear matter energy
loss phenomenology in both p+A and A+A collisions.
