On a floured work surface, divide dough into 8 portions and let the dough rest for approximately 20 minutes. Cut mozzarella balls in half and set on paper towels to drain excess water so your pizza is not soggy in the middle when done.
While dough is resting and cheese is draining, prepare a charcoal, gas or stovetop grill. Grill should be very hot. Position grilling rack 3 or 4 inches from heat source.
With hands, flatten a ball of dough into a circle on baking sheet. Generously coat dough with olive oil spray on both sides. Using fingertips, gently lift dough, and set it on the grill. Cook, covered, until dough has puffed and grill marks appear (about 3 minutes).
Transfer pizza rounds to a baking sheet and place 2 tablespoons pizza sauce, 6 mozzarella halves and cherry tomato halves.
Transfer pizzas with toppings back to grill, cook covered until pizza crust is browned and crisp underneath. Rotate pizzas on grill for even cooking.
Remove from grill and top with fresh basil.