16 fresh black Mission figs, each stemmed and cut into 4 lengthwise slices
1 Tbsp. chopped rosemary
2 cups shredded mozzarella
3/4 cup grated Parmesan
1/2 tsp. kosher salt
1 tsp. ground black pepper
Preheat grill so that 2/3 of grill is on high heat and 1/3 is on low heat. Cut dough into 4 equal pieces. On a lightly floured work surface, roll out each piece of dough into a 6" circle. Cover dough loosely with plastic wrap and let rest 10 minutes.
Coat a large, rimmed baking sheet with oil. Gently stretch a piece of dough into a 9" round, then place on oiled pan to coat both sides. Repeat with other pieces of dough and set aside on another baking sheet.
Working 2 pieces at a time, lift a dough round and drape it over the hot part of the grill. Repeat with second piece. Grill over high heat until seared, about 10 seconds. Using tongs, rotate dough and continue cooking 10 to 20 seconds more. Turn dough over and move to the cooler area. Apply 1/4 of the toppings to each piece of dough, then slide dough back and forth between hot and cool areas to finish cooking dough, melt cheese, and heat toppings, about 30 seconds more. With a large metal spatula, transfer pizzas to a cutting board, slice, and serve. Repeat with remaining dough and toppings.