Oil the pizza pan(s) and set aside.
Prepare the pizza dough, roll it out, and place it in the prepared pan(s).
Preheat the oven to 450 degrees.
Peel and dice the tomatoes, discarding the seeds, and combine with the salt and 1/4 cup oil in a bowl. Spread over the crust.
Bake 15-20 minutes on the lowest oven rack. Remove pizza from the oven and arrange the mozzarella and the Parmesan, if using. Sprinkle with salt and pepper and drizzle on additional olive oil. Return to oven till bubbly, 5-10 minutes. Top with basil and serve immediately.