In a medium skillet over medium heat, add 1 tablespoon of the oil. When it is hot, add the tomato and garlic. Cook down until slightly thickened and some of the liquid has evaporated, about 5 minutes. Season with salt and pepper, to taste, and set aside.
Heat an outdoor grill or grill pan over medium heat. Preheat the broiler.
Pat the pizza dough out into a 12 by 6-inch rectangle and brush with 1 tablespoon of oil. Transfer the dough to the grill and grill, oiled side down, until the dough starts to crisp and turn brown on the bottom side, about 3 minutes. Brush the top with the remaining 1 tablespoon of oil and flip it over and grill for another 3 minutes. Remove from the grill to a sheet pan. Spread it with the tomato sauce and cover with the mozzarella slices. Put it under the broiler and broil until the cheese is melted and bubbling, about 3 minutes. Remove from the broiler, sprinkle with basil leaves, then cut and serve.