Step 1

The dough must sit for at least 24 hours before shaping. We prefer the high protein content of King Arthur bread flour for this recipe, though other bread flours are acceptable. For best results, weigh your ingredients. It’s important to use ice water in the dough to prevent it from overheating in the food processor. Grilled pizza cooks quickly, so it’s critical to have all of your ingredients and tools ready ahead of time. We recommend pargrilling, topping, and grilling in quick succession and serving the pizzas one at a time, rather than all at once.

Step 2

FOR THE DOUGH: Process flour, sugar, and yeast in food processor until combined, about 2 seconds. With processor running, slowly add ice water; process until dough is just combined and no dry flour remains, about 10 seconds. Let dough stand for 10 minutes.

Step 3

Add oil and salt to dough and process until dough forms satiny, sticky ball that clears sides of bowl, 30 to 60 seconds. Transfer dough to lightly oiled counter and knead until smooth, about 1 minute. Divide dough into 3 equal pieces (about 91/3 ounces each). Shape each piece into tight ball, transfer to well-oiled baking sheet (alternatively, place dough balls in individual well-oiled bowls), and coat top of each ball lightly with oil. Cover tightly with plastic wrap (taking care not to compress dough) and refrigerate for at least 24 hours or up to 3 days.

Step 4

FOR THE SAUCE: Pulse tomatoes in food processor until finely chopped, 12 to 15 pulses. Transfer to medium bowl and stir in reserved juice, oil, oregano, sugar, 1/2 teaspoon salt, and pepper flakes. Season with extra sugar and salt to taste, cover, and refrigerate until ready to use.

Step 5

One hour before cooking pizza, remove dough from refrigerator and let stand at room temperature.

Step 6

FOR A CHARCOAL GRILL: Open bottom vent halfway. Light large chimney starter three-quarters filled with charcoal briquettes (4½ quarts). When top coals are partially covered with ash, pour into ring around perimeter of grill, leaving 8-inch clearing in center. Set cooking grate in place, cover, and open lid vent halfway. Heat grill until hot, about 5 minutes.

Step 7

FOR A GAS GRILL: Turn all burners to high, cover, and heat grill until hot, about 15 minutes. Leave all burners on high.

Step 8

While grill is heating, transfer sauce to small saucepan and bring to simmer over medium heat. Cover and keep warm.

Step 9

FOR THE PIZZA: Clean and oil cooking grate. Pour ¼ cup oil onto center of rimmed baking sheet. Transfer 1 dough round to sheet and coat both sides of dough with oil. Using your fingertips and palms, gently press and stretch dough toward edges of sheet to form rough 16 by 12-inch oval of even thickness. Using both your hands, lift dough and carefully transfer to grill. (When transferring dough from sheet to grill, it will droop slightly to form half-moon or snowshoe shape.) Cook (over clearing if using charcoal; covered if using gas) until grill marks form, 2 to 3 minutes. Using tongs and spatula, carefully peel dough from grate, then rotate dough 90 degrees and continue to cook (covered if using gas) until second set of grill marks appears, 2 to 3 minutes longer. Flip dough and cook (covered if using gas) until second side of dough is lightly charred in spots, 2 to 3 minutes. Using tongs or pizza peel, transfer crust to cutting board, inverting so side that was grilled first is facing down. Repeat with remaining 2 dough rounds, adding 1 tablespoon oil to sheet for each round and keeping grill cover closed when not in use to retain heat.

Step 10

Drizzle top of 1 crust with 1 tablespoon oil. Sprinkle one-third of Parmesan evenly over surface. Arrange one-third of mozzarella pieces, evenly spaced, on surface of pizza. Dollop one-third of sauce in evenly spaced 1-tablespoon mounds over surface of pizza. Using pizza peel or overturned rimmed baking sheet, transfer pizza to grill; cover and cook until bottom is well browned and mozzarella is melted, 3 to 5 minutes, checking bottom and turning frequently to prevent burning. Transfer pizza to cutting board, sprinkle with 1 tablespoon basil, drizzle lightly with extra oil, and season with salt to taste. Cut into wedges and serve. Repeat with remaining 2 crusts.