Rub extra virgin olive oil on parchment paper large enough to hold the pressed dough.
Press dough out on oiled parchment paper into the desired shape.
Fire up the grill to medium-high heat. Make sure the grates are clean. Brush grates with oil. Lay the dough down, parchment side up, remove parchment and close the grill for 3-4 minutes, or until dough releases cleanly.
Flip the dough over, spread with pizza sauce, and top with fresh mozzarella and halved tomatoes. Cover the grill and cook an additional 3 minutes, or until mozzarella is melted.
Garnish with flaky salt, cracked black pepper, and basil. Slice and enjoy!