Optical manipulation of objects at the nanometer-to-micrometer scale relies on the precise shaping of a focused laser beam to control the optical forces acting on them. Here, we introduce and experimentally demonstrate surface-shaped laser traps with conformable phase-gradient force field enabling multifunctional optical manipulation of nanoparticles in two dimensions. For instance, we show how this optical force field can be designed to capture and move multiple particles to set them into an autonomous sophisticated optical transport across any flat surface, regardless of the shape of its boundary. Unlike conventional laser traps, the extended optical field of the surface laser trap makes it easier for the particles to interact among themselves and with their environment. It allowed us to optically transport multiple plasmonic nanoparticles (gold nanospheres) while simultaneously enabling their electromagnetic interaction to form spinning optically bound (OB) dimers, which is the smallest case of optical matter system. We have experimentally demonstrated, for the first time, the creation of stable spinning OB dimers with control of their rotational and translational motion across the entire surface. These traveling OB dimers guided by the phase-gradient force work as switchable miniature motor rotors, whose rotation is caused by the combined effects of optical binding forces and optical torque induced by a circularly polarized surface laser trap. The degree of customization of the surface laser traps provides a versatility that can boost the study and control of complex systems of interacting particles, including plasmonic structures as the optical matter ones of high interest in optics and photonics.