1. Prepare outdoor grill for covered direct grilling over medium heat. Meanwhile, spray 2 large cookie sheets with nonstick cooking spray. On work surface, divide dough into 4 equal pieces; spray with nonstick cooking spray. With fingertips, press each piece of dough into a round about 1/8 inch thick (it's okay if dough is not perfectly round). Or, if necessary, with rolling pin, roll each dough piece to 1/8-inch thickness. Transfer two rounds to each prepared cookie sheet; cover loosely with plastic wrap. (Bring dough rounds and remaining ingredients to grill for final pizza assembly.)
2. Place dough rounds on hot grill rack. Cover grill and cook 2 to 3 minutes or until grill marks appear on underside and dough stiffens (dough may puff slightly).
3. With tongs, carefully transfer dough to same cookie sheets, grill-marks side up. Spread pesto on grilled side of dough rounds; top with tomatoes, mozzarella, and pepper. Return dough rounds to grill, toppings side up. Cover grill and cook pizzas 2 to 3 minutes longer or until bottom of dough stiffens and mozzarella begins to melt. Transfer pizzas to cutting board; cut into wedges to serve.