1.

Whisk water and flour in medium bowl until no lumps remain. Microwave until mixture thickens to stiff, smooth, pudding-like consistency that forms mound when dropped from end of whisk into bowl, about 60 seconds, whisking halfway through microwaving.

2.

Add ½ cup (118 grams) water to flour paste and whisk until smooth. Transfer to large bowl. Add salt, sugar, and remaining 1 cup plus 2 tablespoons (265 grams) water and whisk until salt and sugar have dissolved. Whisk in yeast and let sit until yeast has dissolved, about 30 seconds. Add flour. Holding edge of bowl with your hand, use your other hand to mix and squeeze flour into liquid until sticky, shaggy dough forms (dough will be very sticky). Scrape any dough from your hand back into bowl. Cover and let rest for 20 minutes.

3.

Grasping edge of dough with your fingertips, gently lift and fold edge toward middle. Rotate bowl 45 degrees; fold again. Rotate bowl and fold 6 more times (total of 8 folds). Cover and let rest at room temperature for 1½ hours.

4.

Lightly grease rimmed baking sheet. Transfer dough (it will still be very sticky) to well-floured counter and divide into 4 pieces (See A in "Shaping the Dough"). Working with 1 piece at a time, fold edges of dough toward center to form ball (B). Pinch seams closed and flip over. Cup both hands beneath dough and lift dough from counter; slide your hands forward and back against dough to create smooth, taut ball (C). Transfer to prepared sheet. Cover tightly with plastic wrap and refrigerate for at least 18 hours or up to 36 hours.

5.

Process tomatoes and salt with immersion blender or food processor until just smooth, 20 to 60 seconds. (This will yield more sauce than needed in recipe. Sauce can be refrigerated for 2 days or frozen for up to 2 months.)

6.

One hour before baking pizza, remove dough, Pecorino, and mozzarella from refrigerator. (Leave dough covered until using to prevent tops from drying out.) Adjust oven rack 9 inches from broiler element, place baking steel or stone on rack, and heat oven to 550 degrees. Set wire rack in rimmed baking sheet.

7.

When 1 hour has elapsed, uncover 1 dough ball on sheet and sprinkle heaping tablespoon of semolina over top. Smooth semolina over surface of ball, allowing excess to fall around ball. Slide bench scraper under about one-quarter of dough, pushing excess semolina beneath dough. Remove scraper and repeat, working around ball to release it from sheet. Invert ball onto lightly floured counter. Re-cover sheet and set aside.

8.

Lightly flour any sticky areas of dough. Gently press into 7-inch circle, popping any bubbles that are larger than ½ inch. Beginning at center of dough and working upward and outward, use your fingertips to firmly flatten and stretch upper half of round, stopping 1 inch from edge of dough to form rim (D). Slide fingertips of both your hands beneath top of dough and, grasping to avoid rim, flip dough over so rimmed, flattened half is at bottom (E). Repeat flattening and stretching motion until you have 8- to 9-inch round with 1-inch-wide rim (F).

9.

Make fist with your hand and hold it over center of dough. Using your other hand, pick up top of dough round and drape it over your fist, being careful not to compress rim (G). Make fist with hand that lifted dough and place it next to fist under dough, then use both fists to lift dough off counter. Letting dough hang down, gently draw your fists away from each other to stretch dough (H). Rotate dough over your fists while continuing to stretch until dough reaches 11-inch round. Lay dough onto floured peel.

10.

Spread 2 tablespoons tomato sauce over surface of dough. Sprinkle one-quarter of Pecorino evenly over sauce, followed by one-quarter of mozzarella.

11.

Slide pizza onto steel and turn on broiler. Broil until rim is well browned with charred spots and underside of pizza is spotty brown, 4 to 5 minutes. (If top of pizza is well-browned but underside is pale, turn off broiler for final 1 to 2 minutes of cooking and return oven to 550 degrees.) Transfer pizza to prepared rack. Turn off broiler and return oven to 550 degrees.

12.

Top pizza with basil. Let cool until cheese and sauce set up slightly, about 1 minute. Serve immediately. Repeat steps 7 through 12 with remaining dough balls and toppings to make 3 more pizzas.

: Omit Pecorino and basil. For each pizza, after sprinkling with mozzarella, top with 1 to 1½ ounces thinly sliced pepperoni and 1 tablespoon thinly sliced jarred pickled hot or sweet cherry peppers.

: Combine 6 tablespoons tomato sauce with 2 tablespoons heavy cream. Omit Pecorino and basil. Reduce mozzarella to 4 ounces. For each pizza, spread 2 tablespoons tomato-cream mixture over surface of dough. Sprinkle one-quarter of mozzarella evenly over sauce followed by 1 ounce Swedish-style fontina or fontal cut into ½-inch pieces and 1 marinated artichoke heart cut into 8 wedges.

: Omit tomato sauce, Pecorino, and basil. Reduce mozzarella to 4 ounces and add 4 ounces Taleggio, rind removed and cut into ½-inch pieces. Toss 10 ounces white or cremini mushrooms sliced ½ inch thick, 2 thinly sliced garlic cloves, 1 teaspoon extra-virgin olive oil, and pinch of table salt until well combined. For each pizza, drizzle 2 teaspoons extra-virgin olive oil over surface of dough. Sprinkle with one-quarter of mozzarella followed by one-quarter of Taleggio and one-quarter of mushroom mixture. When pizza comes out of oven, sprinkle with lemon zest and lemon juice to taste.