Divide the dough in two. Using your hands or a rolling pin, gently stretch the dough.
For fresh tomatoes: Place fresh tomatoes in boiling water for 10 minutes. Then transfer them to an ice bath for 3 minutes. Peel and chop the tomatoes. Blend for 1 to 2 minutes and add salt.
For canned tomatoes: Blend 3 to 4 whole tomatoes from the can (without the juice) for 1 to 2 minutes and add salt. Tip: Do not use the juice from the can as it will make the sauce too watery.
Cut the mozzarella into thin strips and place them on paper towels. Press the cheese 2 to 3 times to remove excess moisture.
Spread 3 to 4 tablespoons of the tomato sauce on the pizza dough. Add a drizzle of olive oil.
Bake at 500°F on a pizza stone in the oven or barbecue for 6 minutes.
Spread the cheese and basil on the partially baked dough.
Bake another 4 to 5 minutes in the barbecue.
If you’re making a second pizza, the cooking time will be shorter because the pizza stone will already be hot from the first pizza.