Shaping the topology of light, by way of spin or orbital angular momentum engineering, is a powerful tool to manipulate matter on the nanoscale. Conventionally, such methods focus on shaping the incident beam of light and not the full interaction between the light and the object to be manipulated. We theoretically show that tailoring the topology of the phase space of the light particle interaction is a fundamentally more versatile approach, enabling dynamics that may not be achievable by shaping of the light alone. In this manner, we find that optically asymmetric (Janus) particles can become stable nanoscale motors even in a light field with zero angular momentum. These precessing steady states arise from topologically protected anticrossing behavior of the vortices of the optical torque vector field. Furthermore, by varying the wavelength of the incident light, we can control the number, orientations, and the stability of the spinning states. These results show that the combination of phase-space topology and particle asymmetry can provide a powerful degree of freedom in designing nanoparticles for optimal external manipulation in a range of nano- optomechanical applications.