Preheat or prepare grill to high heat (450° to 500°).
If using pizza dough, roll out pizza dough or press with fingertips on a very lightly floured countertop to between 1/4-inch and 1/2- thick into a rectangle. Don’t worry about shaping it into a perfect rectangle. This is the “artisan” look.
Sprinkle cornmeal on a large, flat baking sheet or turn a baking sheet with a rim on it over and use the underside. Place the pizza crusts or Naan bread on the baking sheet and brush the tops of each crust lightly with 1 teaspoon of oil.
Brush the grill lightly with a silicone grill brush. Slide the pizza crusts onto the grill, using tongs to help pull it onto the grill. Close the lid and grill for just 1 to 2 minutes or until grill marks start to show. You will grill this side one more time with toppings on it.
Using tongs, flip the crust over. Close the lid and grill 2 minutes or until grill marks show on the bottom. Using tongs, place the crusts back on the baking sheet, cornmeal side down.
Spread chile garlic sauce evenly over both crusts. Spread Thai peanut sauce over chile garlic sauce. Arrange chicken evenly on crusts and sprinkle with bell pepper and carrots.
Sprinkle cheese evenly over carrots.
Slide pizzas back onto the grill with tongs. The heat should have risen back up to 450° to 500°.
Close the lid and grill for 1 minute or until cheese melts. Using tongs, slide pizzas back onto the baking sheets. Sprinkle with peanuts, green onions, and cilantro. Let stand 2 to 3 minutes, then transfer to a cutting board and slice before serving….unless one whole pizza is your serving, then just dive in!