- In food processor fitted with metal blade, process 3 cups bread flour, 2 tablespoons sugar, and ½ teaspoon instant or rapid-rise yeast until combined, about 2 seconds.
- With machine running, slowly add 1⅓ cups ice water through feed tube; process until dough is just combined and no dry flour remains, about 10 seconds. Let dough stand 10 minutes.
- Add 1 tablespoon vegetable oil and 1½ teaspoons table salt to dough and process until dough forms satiny, sticky ball that clears sides of workbowl, 30 to 60 seconds.
- Remove dough from bowl and 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.
- In food processor, combine 1 can whole peeled tomatoes, drained and liquid discarded; 1 tablespoon extra-virgin olive oil; 1 teaspoon red wine vinegar; 2 medium garlic cloves, minced; 1 teaspoon table salt; 1 teaspoon dried oregano; and ¼ teaspoon ground black pepper. Process until smooth, about 30 seconds. Transfer to medium bowl or container and refrigerate until ready to use.
- 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 ½ cup tomato sauce in thin layer over surface of dough, leaving ¼-inch border around edge. Sprinkle ¼ cup Parmesan evenly over sauce, followed by 1 cup shredded whole-milk mozzarella.
- Slide pizza carefully onto stone and bake until crust is well browned and cheese is bubbly and beginning to brown, 10 to 12 minutes, rotating pizza halfway through.
- Remove pizza and place on wire rack for 5 minutes before slicing and serving. Repeat shaping, topping, and baking second pizza.
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