Meanwhile, place dough on a lightly floured surface. Divide into 4 pieces. Roll each piece into an 8-inch round crust, about 1/4 inch thick. Place crusts on a floured baking sheet. Carry crusts and toppings out to the grill.y crusts on grill (they won't stay perfectly round). Cover grill and cook until crusts are lightly puffed and undersides are lightly browned, about 3 minutes.
Using tongs, flip crusts. Immediately spread pesto over crusts. Top with tomatoes. Sprinkle with feta and pepper. Cover grill and cook until the undersides are lightly browned, about 3 minutes more. Sprinkle with basil and serve immediately.