For the Dough: In a food processor fitted with metal blade, process flour, sugar and yeast until combined, about 2 seconds. With machine running, slowly add water through feed tube; process until dough is just combined and no dry flour remains, about 10 seconds. Let dough stand 10 minutes.

Add oil and salt to dough and process until dough forms satiny, sticky ball that clears sides of work bowl, 30 to 60 seconds. Remove dough from bowl, knead briefly on lightly oiled countertop until smooth, about 1 minute. Shape dough into tight ball and place in large, lightly oiled bowl. Cover tightly with plastic wrap and refrigerate for at least 24 hours and up to 3 days.

For the Sauce: Process all ingredients in food processor until smooth, about 30 seconds. Transfer to medium bowl or container and refrigerate until ready to use.

To Bake the Pizza: One hour before baking pizza, adjust oven rack to second highest position (rack should be about 4 to 5 inches below broiler), set pizza stone on rack, and heat oven to 500 degrees. Remove dough from refrigerator and divide in half. Shape each half into smooth, tight ball. Place on lightly oiled baking sheet, spacing them at least 3 inches apart; cover loosely with plastic wrap coated with nonstick cooking spray; let stand for 1 hour.

Coat 1 ball of dough generously with flour and place on well-floured countertop. Using fingertips, gently flatten into 8-inch disk, leaving 1 inch of outer edge slightly thicker than center. Using hands, gently stretch disk into 12-inch round, working along edges and giving disk quarter turns as you stretch. Transfer dough to well-floured peel and stretch into 13-inch round. Using back of spoon or ladle, spread 1/2 cup tomato sauce in thin layer over surface of dough, leaving 1/4-inch border around edge. Sprinkle 1/4 cup Parmesan evenly over sauce, followed by 1 cup mozzarella. Slide pizza carefully onto stone and bake until crust is well browned and cheese is bubbly and beginning to brown, 10-12 minutes, rotating pizza halfway through. Remove pizza and place on wire rack for 5 minutes before slicing and serving. Shape, top and bake second pizza.