Unroll dough onto work surface, stretching to form 12x12-inch square. Cut into 4 equal pieces. Using large spatula, transfer dough to grill rack; cover and grill until bottoms are brown, about 4 minutes. Turn squares over and immediately top each with tomato mixture, leaving 1/2-inch border. Cover and grill until pizza bottoms are brown and cheese is melted, about 4 minutes. Sprinkle pizzas with Parmesan and serve.