  We theoretically investigate the ground states and the spectrum of elementary
excitations across the superfluid to droplet crystallization transition of an
oblate dipolar Bose-Einstein condensate. We systematically identify regimes
where spontaneous rotational symmetry breaking leads to the emergence of a
supersolid phase with characteristic collective excitations, such as the Higgs
amplitude mode. Furthermore, we study the dynamics across the transition and
show how these supersolids can be realized with standard protocols in
state-of-the-art experiments.
