Place a pizza stone on a barbecue grate. Preheat the grill, setting the burners to high.
On a lightly floured surface, divide the dough into 4 pieces. Roll out 1 piece of dough at a time into a 9-inch (23 cm) disc. Place the disc on a sheet of parchment paper. Cover with tomatoes and cheese. Season with salt.
Place the pizza on the hot stone with the parchment paper. Close the lid and cook for 6 to 10 minutes, or until the crust is golden brown and the cheese has melted. Remove from the heat. Let rest 1 minute. Garnish with fresh basil leaves. Season with pepper. Drizzle with olive oil. Repeat with the remaining pizzas.
If you don’t have fresh mozzarella on hand, use bocconcini.