Quantum simulation with ultracold atoms has opened the avenue to probe non-equilibrium quantum many body dynamics in new parameters regimes and with completeley new detection techniques. Specifically, we utilize the high-resolution, single-spin sensitive detection afforded by a quantum gas microscope to track the out-of-equilibrium dynamics of Heisenberg quantum magnets. In recent experiments, we have tracked the evolution of one-dimensional Heisenberg spin chains starting from initial spin-domain wall states. We demonstrate superdiffusive spin transport in this regime by monitoring the polarization transfer in the system over time. Additionally, by accessing the full counting statistics of transported spins, we find strong supporting evidence for the conjecture that transport in the XXZ chain at the Heisenberg point indeed falls in the KPZ universality class.