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In this work, we study the jet momentum broadening in an inhomogeneous dense QCD medium. The transverse profile of this nuclear matter is described within a gradient expansion, and we focus on the leading gradient contributions. The leading parton is allowed to interact multiple times with the background through the soft gluon exchanges. We derive the associated final particle distribution using both the GLV opacity series and the BDMPS-Z formalism. We further discuss the modified factorization of the initial and final state effects and its consequences for phenomenological applications in the context of heavy-ion collisions and deep inelastic scattering. Finally, we present the broadening probability (describing the final state effects) in several limiting regimes, and give its numerical estimates for phenomenologically motivated sets of parameters.