  We report on the emergence of bulk, valley-polarized currents in
graphene-based devices, driven by spatially varying regions of broken
sublattice symmetry, and revealed by non-local resistance ($R_\mathrm{NL}$)
fingerprints. By using a combination of quantum transport formalisms, giving
access to bulk properties as well as multi-terminal device responses, the
presence of a non-uniform local bandgap is shown to give rise to
valley-dependent scattering and a finite Fermi surface contribution to the
valley Hall conductivity, related to characteristics of $R_\mathrm{NL}$. These
features are robust against disorder and provide a plausible interpretation of
controversial experiments in graphene/hBN superlattices. Our findings suggest
both an alternative mechanism for the generation of valley Hall effect in
graphene, and a route towards valley-dependent electron optics, by materials
and device engineering.
