Processing soft disordered solids such as glassy colloidal suspensions and pastes invariably involves inducing flow, and understanding how the fluidized materials turn back into solids is crucial for their application. Unlike liquids where stress decays quickly when flow ceases, soft disordered solids can display a protracted recovery in which stress slowly decreases to a value, known at the residual stress, that can depend on aspects of the preceding flow like the shear rate. This dependence provides a mechanism for tailoring soft disordered solids with shear. While numerous rheology studies have characterized the macroscopic nature of stress relaxation in soft disordered solids, little is known about the underlying microscopic structural dynamics. In this talk, we report x-ray photon correlation spectroscopy (XPCS) experiments with in situ rheometry performed on a soft glass composed of a concentrated suspension of charged silica nanoparticles (Ludox). The XPCS measurements characterize the particle-scale and mesoscale motions within the glass following the cessation of flow-inducing shear that underlie the subsequent slow decay of the stress. The XPCS correlation functions indicate these microscopic dynamics are anisotropic, with superdiffusive particle motion along the direction of the preceding shear that persists to surprisingly large waiting times after flow cessation and that is accompanied by highly intermittent motion in the perpendicular (vorticity and shear gradient) directions. The close correspondence between these dynamics and the stress relaxation is demonstrated by an intriguing, linear scaling between the decay rate of the correlation functions and the rate of stress decay.