  Atomically-thin materials based on transition metal dichalcogenides and
graphene offer a promising avenue for unlocking the mechanisms underlying the
spin Hall effect (SHE) in heterointerfaces. Here, we develop a microscopic
theory of the SHE for twisted van der Waals heterostructures that fully
incorporates twisting and disorder effects, and illustrate the critical role of
symmetry breaking in the generation of spin-Hall currents. We find that an
accurate treatment of vertex corrections leads to a qualitatively and
quantitatively different SHE than that obtained from popular approaches like
the ``$i\,\eta$'' and ladder approximations. A pronounced oscillatory behavior
of skew-scattering processes with twist angle, $\theta$, is predicted,
reflecting a non-trivial interplay of Rashba and valley-Zeeman effects and
yields a vanishing SHE for $\theta = 30^\circ$ and, for graphene-WSe$_2$, an
optimal SHE for $\theta \approx 17^\circ$. Our findings reveal disorder and
broken symmetries as important knobs to optimize interfacial SHEs.
