We propose a technique that allows to laser cool a nanomechanical resonator mode to its motional ground state. The method is based on resonant laser excitation of a phonon sideband of an embedded self-assembled quantum dot. The strength of this sideband coupling is determined directly by the difference between the electron-phonon couplings of the initial and final states of the quantum dot (QD) optical transition. When compared with the analogous sideband-cooling of a trapped-ion (TI), we find novel quantum interference effects in the cooling cycle and that the finite Q-value can lead to regimes where the final occupancy is proportional to the initial one -- with their ratio determined by the product of the "effective Lamb-Dicke" parameter and the Q-value. The interactions underlying this cooling scheme also provide a tool-box for quantum state engineering in these systems.