Rub 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!