For the dough: Combine the sugar, oil, yeast and 2 cups cold water in the bowl of a stand mixer fitted with a dough hook. Let the mixture sit until foamy, about 10 minutes.
Mix the flour and salt in a bowl. With the motor running, slowly add the flour mixture to the yeast mixture. Keep mixing until a smooth, elastic dough forms, about 10 minutes.
Transfer the dough to a lightly greased baking sheet and cover loosely with plastic wrap. Let sit at room temperature for 1 hour.
Divide the dough into four 12-ounce pieces and shape into balls. Transfer the balls to a lightly greased 9-by-13-inch baking dish and brush with oil. Cover tightly with plastic wrap and refrigerate for at least 24 hours.
For the sauce: Remove each tomato from the can and reserve 3 cups of the puree. Cut the tomatoes in half and, using your fingers, remove and discard the seeds (don't rinse). Place the tomatoes in a food processor and pulse until just crushed but not pureed. (Alternatively, crush the tomatoes by hand or pass them through a food mill.) Transfer the tomato sauce to a bowl and stir in the reserved 3 cups of puree and some salt.
For the pizza: Place a pizza stone under the oven broiler. Preheat the broiler for 30 minutes.
Working in four batches, dust a ball of dough heavily with semolina. Using your fingertips, press the dough from the center out, into a 10-inch circle, about 1/4-inch thick, leaving a 1-inch thick crust around the edges.
Hold the dough straight up, and with your fingertips circling the crust, let the dough naturally fall. Slide your fingers around crust in a circular motion (like you would turn a steering wheel) until the dough in the center is stretched to about 1/8-inch thick. Repeat for the remaining dough balls. Transfer the dough to a semolina-dusted pizza peel.
Spread each pizza with about 1/2 cup sauce evenly over center of the dough, distribute a quarter each of the cheese and basil leaves, and drizzle with oil. Slide a pizza onto the stone and broil until the cheese melts and the crust is puffed and charred in spots, 3 to 4 minutes. Repeat for the remaining pizzas. Serve hot. Enjoy!
The 24 hour resting period of this dough is essential to retard the formation of gluten, resulting in the signature Neapolitan chewy, puffed pizza.
This recipe was provided by a chef, restaurant or culinary professional. It has not been tested for home use.