Divide the dough into two pieces and form each piece into a ball. Oil a quarter sheet pan (9-by-13-inch) with oil. Dust a work surface and roll and stretch the dough until it’s about the size of the sheet pan. Transfer the dough to the sheet pan and press it until it fills the pan. Cover with plastic and let proof at room temperature for 1 hour. Repeat with the remaining dough.
Preheat oven to 475°. Divide the tomato sauce between the two pizzas, using the back of a spoon to cover the top of the pie. Scatter half of the mozzarella over each pie. Sprinkle half of the oregano over each pie. Bake the pies in the center of the oven until edges are crispy and browned and tomato sauce has thickened, about 15 minutes. Sprinkle each pie with ¼ cup of Parmesan; half of the basil, fried garlic and salt; and a pinch of red-pepper flakes. Using a large spatula, transfer the pies to a cutting board, cut each into 6 pieces and serve.