  An outstanding challenge in large-scale quantum platforms is to
simultaneously achieve strong interactions, giving rise to the most interesting
behaviors, and local addressing -that can probe them. In the context of
correlated phases, local addressing enables one to directly probe the nature of
the system's order. Meanwhile, for out-ofequilibrium dynamics, such addressing
allows the study of quantum information spreading and operator growth. Here, we
introduce a novel technique that enables the measurement of local correlation
functions, down to single-site resolution, despite access to only global
controls. Our approach leverages the intrinsic disorder present in a
solid-state spin ensemble to dephase the nonlocal components of the correlation
function. Utilizing this toolset, we measure both the spin and energy transport
in nuclear spin chains. By tuning the interaction Hamiltonian via Floquet
engineering, we investigate the cross-over between ballistic and diffusive
hydrodynamics. Interestingly, when the system is both interacting and
(nearly-)integrable, we observe the coexistence of diffusive spin transport
with ballistic energy transport.
