Are there any dishes that can only be cooked with a microwave?
Yes!

In 1969, the physicist Nicholas Kurti gave a talk in which he demonstrated a variant of Baked Alaska called "Frozen Florida": a shell of frozen meringue around a center of hot liquor. This was done by chilling the meringue and the liquor together, then cooking in a microwave oven which had a rotating platter and no stirring fan. Because the microwave beam was always heating the center but only intermittently heating any given part of the meringue, and because the meringue was low-density and frozen, the liquor could be heated while the meringue remained frozen.

(The idea was broadly similar to, and presumably inspired by, radiation therapy for cancer, in which a tightly focused beam of radiation revolves around a particular spot which may be deep inside the subject's body: only that single spot is always being energized by the beam, so it receives much more energy than the rest of the body does.)