Instructions

for the dough

Process 16½ ounces King Arthur bread flour, 1 tablespoon sugar, and ¼ teaspoon instant yeast in food processor until combined, about 2 seconds.
With processor running, slowly add 11 ounces ice water; process until dough is just combined and no dry flour remains, about 10 seconds. Let dough stand for 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 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 9⅓ 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.

for the sauce

Drain 14-ounce can whole peeled tomatoes and reserve juices. Pulse tomatoes in food processor until finely chopped, 12 to 15 pulses. Transfer to medium bowl and stir in reserved juice, 2 tablespoons extra-virgin olive oil, 2 teaspoons minced fresh oregano, ½ teaspoon sugar, ½ teaspoon table salt, and ¼ teaspoon red pepper flakes. Season with extra sugar and salt to taste, cover, and refrigerate until ready to use.
One hour before cooking pizza, remove dough from refrigerator and let stand at room temperature.

for the grill

If using charcoal grill, open bottom vent halfway. Light large chimney starter three-quarters filled with charcoal briquettes (4½ quarts). If using gas grill, turn all burners to high, cover, and heat grill until hot, about 15 minutes. Leave all burners on high.
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.
While grill heats, tear 8 ounces fresh whole-milk mozzarella cheese into bite-sized pieces and set aside. Transfer sauce to small saucepan and bring to simmer over medium heat. Cover and keep warm.

for the pizza

Clean and oil cooking grate. Pour ¼ cup extra-virgin olive 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.)
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.
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 extra-virgin olive oil to sheet for each round and keeping grill cover closed when not in use to retain heat.
Drizzle top of 1 crust with 1 tablespoon extra-virgin olive oil. Sprinkle ½ cup grated Parmesan cheese evenly over surface.
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 shredded fresh basil, drizzle lightly with extra-virgin olive oil, and season with coarse sea salt to taste. Cut into wedges and serve. Repeat with remaining 2 crusts.