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1
Preheat a grill to medium-high heat.
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2
In a medium bowl, stir the chopped tomatoes with 1 tablespoon olive oil, the vinegar, 1/2 teaspoon salt and 1/4 teaspoon pepper.
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3
Toss well and let stand to become juicy and soft while you make the pizza.
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4
Divide the dough into 2 pieces.
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5
Stretch each piece of dough into a large rectangle on a lightly floured work surface using your hands or a rolling pin, about 10-inches long by 6-inches wide.
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6
Transfer to the back of a large baking sheet using your hands and reshape the rectangle, if necessary.
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7
In a small bowl, mix the remaining 3 tablespoons oil with the grated garlic and lightly brush the top of each piece of dough.
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8
Working with one piece of dough at a time, place the dough, oiled-side down, on the grill until the dough puffs and the bottom is lightly charred with deep grill marks, 2 to 3 minutes.
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9
Flip the dough, using heatproof tongs and a spatula.
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10
Brush what is now the top of the pizza with half the oil and sprinkle with half the Parmesan.
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11
Grill until the cheese is melted and the pizza is crisped, about 2 minutes.
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12
Transfer to a large cutting board.
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13
Repeat with the second dough rectangle.
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14
Cut the grilled pizza into 2-inch wide strips and cut each in half crosswise.
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15
Mash the tomato mixture, using a potato masher, to form a chunky sauce and stir in the basil.
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16
Serve the flatbread strips with the tomato sauce on the side.
