Coat the pizza dough with 1 tablespoon of the olive oil. Using your hands, rub the oil onto the outside of the dough while carefully stretching it into a circle 12-14 inches (30-35 cm) in diameter. Place the oiled pizza dough onto the preheated grill and quickly brush the top with the remaining tablespoon of olive oil. Close the grill and allow pizza dough to cook for 3-4 minutes.
After 4 minutes, check the pizza. Large bubbles should be forming across the top of the dough. Using a large spatula or set of tongs, flip the dough over. Reduce the heat to low and add the sauce, cheese, and basil to the pizza. Increase the heat back to high and close the grill. Cook the pizza for 5-6 minutes, until the cheese has melted and the bottom of the crust is lightly charred.
Cook the pizza for 5-6 minutes more, until the cheese has melted and the bottom of the crust is lightly charred.