Preheat oven to 475°F. Brush bottom of a large rimmed baking sheet with olive oil. Press and stretch pizza dough evenly to make a large round. (If dough resists at first, let it rest for a minute and then continue.) Sprinkle with mozzarella and half of Parmesan, leaving a 1/2-inch plain border.
Arrange artichoke hearts, mushrooms, sun-dried tomatoes and peppers as desired on pizza. Sprinkle with remaining Parmesan. Bake pizza until underside of dough is golden (lift pizza carefully with a spatula to take a peek) and cheese is bubbling, 15 to 20 minutes. Let stand for 5 minutes on a wire rack before slicing and serving. Offer garlic powder or crushed red pepper flakes on the side.