Use a charcoal or gas grill with a cover. Pile the coals or lava rocks high on one side of grill and place them sparsely on other side. Top with grate. Light grill and let coals heat up.
Divide dough into 8 pieces and stretch each piece by hand until 3 to 4 inches in diameter. Let rise a second time, covered, on a baking sheet. Place as many rounds as you can fit without crowding on hot side of grill. Grill for 1 to 2 minutes or until bottoms are light brown. Flip over and grill for 30 seconds to 1 minute, or until top sides are colored.
Flip again and place pizzas on cool side of fire. Top with cheeses, sprinkle with pepper and drizzle with oil. Cover grill and cook for 3 to 5 minutes, or just until cheese melts and browns slightly. Check once or twice to make sure underside is not getting burned; if it is, push coals away from the cool side of the fire. If cheese doesn't brown, you can run it under a hot broiler for a minute. Serve immediately.