1. Preheat your grill so that one side is on high and the other is on medium. If using charcoal, set it up for two-tiered grilling, arranging the coals in a double layer on one side and in a single layer on the other.
2. Cut the tomatoes crosswise into 1/2-inch-thick slices. Brush each with a small amount of oil and season with salt and pepper. Quickly char the tomato slices on the hot side of the grill, turning with a spatula, about 2 minutes per side. Transfer to a plate and let cool.
3. Generously oil a large baking sheet and place one disk of dough on it. Use the fingers and palms of your hands to stretch out the dough into a 13 3 9 inch rectangle (it needn’t be too even). This stretching technique takes a little practice, so don’t be discouraged if your first rectangle isn’t picture perfect. Stretch out the other disk of dough on another oiled baking sheet.
4. Working with one stretched-out piece at a time, using both hands, gently lift the dough rectangle from the baking sheet. Drape it onto the grill over the hottest part of the fire. Within a minute or so, the underside of the dough will crisp, darken, and harden and the top will puff slightly. Turn the dough over with tongs or two spatulas and move it to the cooler side of the grill.
5. Quickly brush the top of the pizza with 1 tablespoon of the oil. Scatter half the garlic over, then sprinkle with half the cheese and arrange half the tomato slices and basil leaves on top. Drizzle the surface of the pizza with another tablespoon of oil and season with salt and pepper.
6. Slide the pizza back over to the hotter part of the grill, rotating to ensure even cooking. Cook until the underside is slightly charred and the cheese is melted on top, 2 to 4 minutes.
7. Remove the pizza from the grill, cut into serving pieces, and serve while you repeat the procedure with the second stretched-out piece of dough.
Makes 2 pizzas serves 8 as an appetizer, 2 to 4 as an entrée
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