1 large ball fresh mozzarella (packed in water), sliced thinly
3/4 cup packed fresh whole basil leaves
Coarse kosher or sea salt, to taste
1/4 cup grated Parmesan
Extra-virgin olive oil as needed
Garnish: fresh basil leaves (optional)
Bring your grill to medium heat and set the rack about 4 inches above the heat source. Roll or lightly press each dough ball into a flat round, lightly flouring the work surface and the dough as necessary. Let the rounds sit for a few minutes; this will relax the dough and make it easier to roll out. Roll or pat out the dough on a well-floured pizza peel, as thinly as you like, turning occasionally to prevent it from sticking.
Place the dough directly on the grill. Grill until nicely browned on the bottom, about 5 minutes. Brush with olive oil and turn. Top the pie with tomatoes, mozzarella, basil leaves, salt, and Parmesan. Drizzle with olive oil. Cover and grill until the cheese melts.