Clearly dwarves eat gems and precious metals, which is why they're always digging around looking for the stuff.
But probably mushrooms, lots and lots of mushrooms and other fungi. Violet fungus souffle, hearty dark breads made of brown mold, and for desert: black pudding. Of course they follow the universal rule of not eating anything with green slime on it.
Then there's the question of whether the dwarves really live underground, or if they hide their towns so well and spend so much time there that people assume they live under the mountains.