Heat grill to high. Roll the dough into 2 (10-inch circles). Brush with olive oil and season with salt and pepper. Transfer dough to grill. When bottom side is mostly cooked through, brush with 2 tablespoons olive oil and sprinkle evenly with grated cheese, red pepper flakes, oregano, and salt and pepper. Let cook until dough is cooked through and slightly charred. Remove from grill, garnish with fresh basil, and cut into pieces.