  We analyze the cooling of a mechanical resonator coupled to an ensemble of
interacting two-level systems via an open quantum systems approach. Using an
exact analytical result, we find optimal cooling occurs when the phonon mode is
critically coupled ($\gamma \sim g$) to the two-level system ensemble. Typical
systems operate in sub-optimal cooling regimes due to the intrinsic parameter
mismatch ($\gamma \gg g$) between the dissipative decay rate $\gamma$ and the
coupling factor $g$. To overcome this obstacle, we show that carefully
engineering the coupling parameters through the strain profile of the
mechanical resonator allows phonon cooling to proceed through the dark
(subradiant) entangled states of an \emph{interacting} ensemble, thereby
resulting in optimal phonon cooling. Our results provide a new avenue for
ground-state cooling and should be accessible for experimental demonstrations.
