Making grilled pizza is a bit of a participatory event, and is best done when guests are outside, milling near the grill. Guests can get involved in customizing their pizzas or requesting combinations. Use whatever toppings you like in addition to the tomatoes.
Build a fire in a grill and let it burn until the coals are glowing and beginning to cool down. Bank the coals on 1 side of the grill to create a hot side and a cooler side.
Divide a 1-pound piece of thawed frozen pizza dough into 2 pieces. Roll each piece out on a floured surface. Place 1 piece of dough on the hot side of the grill for 1 to 2 minutes, just to toast it slightly. Flip the dough and move it to the cooler side of the grill.
Place the other piece of dough on the hot spot, and grill for 1 to 2 minutes. Use tongs to pull both pieces to the cooler side of the grill. Flip the dough over and dress it with sliced tomatoes, fresh mozzarella, a drizzle of olive oil, and a sprinkle of salt.
Cover the grill and cook the pizza until the cheese melts, about 5 minutes. Top with torn basil leaves. Repeat with the second piece of dough.