Step 1

Arrange a rack in the bottom third of the oven. Place a heavy rimmed baking sheet upside-down on the rack, and heat the oven to 450°F.

Step 2

Make the sauce: Place the garlic in a food processor fitted with the blade attachment and pulse until coarsely chopped, 2 to 3 pulses. Add the tomatoes and their juices, olive oil, sugar, vinegar, salt, and pepper and process until puréed or to desired consistency, 20 to 30 seconds; set aside.

Step 3

Divide the pizza dough into two pieces. If the dough is sticky, dust with a little bit of all-purpose flour. Dust a 12-inch piece of parchment paper with cornmeal and place the dough on it. Use the heel of your hand to press the dough flat. Work from the middle out to shape it into a 10-inch round with your hands or a rolling pin. The dough will stick to the parchment; if it starts to shrink back, wait a few minutes to let it relax and continue shaping.

Step 4

Brush the dough with 1 teaspoon of the olive oil, then spread 1/4 cup of the sauce into a thin layer onto dough, leaving a 1/2-inch border. Carefully remove the preheated baking sheet from the oven and use the parchment paper to slide the pizza onto the back of the baking sheet.

Step 5

Bake for 4 minutes. Top the pizza with half of the mozzarella, leaving some space between the slices. Bake until the crust is golden brown and crisp and the cheese melts, 6 to 7 minutes more.

Step 6

Remove the pizza from the oven. Immediately drizzle with 2 teaspoons of the olive oil. Scatter half of the basil on the pizza and sprinkle with half of the Parmesan. Cool for 2 minutes before slicing and serving. Repeat with the remaining dough and toppings.