Place a pizza stone in the oven and preheat it to 550°, or your oven’s highest temperature.
Place 1 cup shredded rotisserie chicken in a bowl and toss with 3 tablespoons of barbecue sauce.
Allow dough to come to room temperature then, on a lightly floured work surface, stretch and gently press into a large circle, about 16 inches. Carefully transfer dough to the pizza stone and bake for 4 minutes.
Remove dough from the oven and top with remaining barbecue sauce. Follow with chicken, both cheeses, and the thinly sliced onion.
Bake for another 4-5 minutes, or until the cheese is bubbly and the crust is brown.
Remove from the oven, top with cilantro, and serve.
