Place the dough on a floured cutting board and, using your hands, gently stretch it into a 12- to 14-inch square or disk, making sure that it retains the same thickness throughout (more or less). (Alternatively, you can roll it out to a 12-inchsquare or circle.)
Brush the top of the dough with olive oil, making sure to get all the way to the edges. Carefully transfer the dough to the grill, oiled-side down, and grill for 3 minutes or until it puffs a bit and the bottom shows grill marks.
Using long-handled tongs or a pizza peel, transfer the dough to a clean large cutting board, grill marks facing up. Brush the grilled dough lightly with olive oil. Working quickly, spread about ½ cup of sauce on the dough and top with the cheese.
Using your large spatula or pizza peel, return the topped crust to the grill. Close the grill lid, turn down the heat to medium or medium-high, and cook for 3 to 5 minutes or until the cheese has melted.
Remove the pizza from the grill and let it rest for 5 minutes, then garnish with the basil, a drizzle of olive oil, and a pinch or two of salt and pepper. Slice and serve.