The modification of the hard core of jets in a dense QCD medium is studied. In particular, we consider partons which possess a virtuality somewhat larger than the multiple scattering scale of the medium (qτ , where q is the transverse broadening jet transport coefficient, and τ is the formation length of a particular emission). We delineate the region of parameter space where the higher-twist approach is applicable, and derive the in-medium DGLAP evolution equation. We study a region in parameter space where this is the dominant mechanism of energy loss. We argue that such a regime is pervasive in most cases of jets in A-A and future e-A collisions, and controls the modification of the hard core of jets and the leading single particle spectrum at high transverse momentum (p T ).