Arrange oven racks in the lower and upper thirds of the oven. Heat oven to 475° F.
Roll out the dough on a well-floured surface to make two 12-inch squares or rounds. Transfer to two ungreased baking sheets.
Top the dough with the tomatoes, mushrooms, and olives. Drizzle with the oil and season with ½ teaspoon salt and ¼ teaspoon pepper.
Bake the pizzas for 10 minutes. Remove from oven.
Top the pizzas with the mozzarella. Return to oven and bake 3 to 5 minutes or until the cheese is melted and the edges of the pies are lightly browned.