Heat gas or charcoal grill to medium heat. Cut 14 x 14-inch piece of heavy duty foil; spray foil with cooking spray. Place dough on foil; starting at center press dough to 12-inch round. Place dough on grill, foil side down. Cook, uncovered, 3 minutes or until bottom of crust is light golden brown. Remove from grill.
Using wide spatula, flip crust over so uncooked side is down. Brush pesto over pizza crust. Sprinkle 1/2 cup of the mozzarella cheese over pesto. Arrange tomato slices and basil leaves on cheese. Sprinkle with remaining 1/2 cup mozzarella cheese and the Parmesan cheese.
Place pizza onto grill, foil side down. Cook, covered, an additional 3 to 4 minutes or until crust is golden brown and cheese begins to melt.