Polenta Bites with Wild Mushrooms and Fontina

Name: Polenta Bites with Wild Mushrooms and Fontina
Ingredients: 4 pounds prepared polenta, sliced into 1/2-inch-thick rounds (about 30 rounds); 2 tablespoons extra-virgin olive oil, plus more for brushing; 1/4 cup (1/2 stick) unsalted butter; 2 pounds assorted wild mushrooms (such as oyster, crimini, and/or stemmed shiitake), cut into thick slices; 2 shallots, thinly sliced; 1/4 cup Sherry vinegar; 1 3/4 teaspoons kosher salt; 1/2 teaspoon freshly ground black pepper; 1/2 teaspoon crushed red pepper flakes; 1/2 cup chopped parsley leaves; 4 ounces Fontina cheese, coarsely grated (about 1 cup)