Place a pizza stone, baking tiles or an inverted baking sheet on the lowest rack of the oven; preheat to 500°F or the highest oven setting.
Divide dough into 8 pieces. Using your fists, stretch one piece into a 6-inch round. Alternatively, with a rolling pin, roll out on a lightly floured surface. (Keep remaining dough covered with a towel or plastic wrap.) Place on a cornmeal-dusted pizza peel or an inverted baking sheet, using enough cornmeal so that the dough slides easily. Stretch or roll a second round of dough and place beside the first.
Sprinkle 2 tablespoons cheese over each round of dough. Arrange 1/2 cup tomatoes, 1/4 cup zucchini, 1 cup mushrooms and a few onion slices over the cheese. Sprinkle 1 teaspoon basil over the top and season with salt and pepper.
Carefully slide the pizzas onto the heated pizza stone, baking tiles or baking sheet and bake until the bottoms are crisp and browned, 10 to 14 minutes. Repeat with the remaining dough and toppings.