After preparing grilled tomatoes, reduce grill to low. Divide pizza dough into four pieces. On a lightly floured work surface, shape dough into rough 12-inch-long ovals. Alternate between rolling the dough with a pin and stretching it with your hands. If it tears, pinch dough together to patch.
Place dough on grill. Cook until lightly charred on one side, 3 to 4 minutes; press lightly with a spatula to deflate any air bubbles.
Flip dough; layer with cheese and grilled tomatoes, dividing evenly. Cover grill; cook until cheese melts and bottoms of crusts are charred, 4 to 6 minutes. Garnish with basil.