Grilled Flatbreads with Mushrooms, Ricotta and Herbs

extra-virgin olive oil, plus more for brushing and drizzling

oyster and shiitake mushrooms, thinly sliced (2 cups)

shallot, minced

garlic clove, minced

dry white wine

Salt

Freshly ground pepper

balls of pizza dough, at room temperature

fresh ricotta cheese (8 ounces)

coarsely chopped chervil

coarsely chopped chives

coarsely chopped flat-leaf parsley

coarsely chopped tarragon