1Mix warm water, yeast, and a pinch of salt in a bowl; let sit 5 minutes until foamy.
2Add flour, salt, and olive oil to the yeast mixture. Stir until shaggy, then knead by hand or with a mixer for 5 minutes until smooth. Let dough rest while you prep toppings.
3Slice onion into thin strips. Heat 1 tablespoon olive oil in a cast iron skillet over medium-high heat and cook onions, stirring occasionally, until golden and soft, about 8 minutes. Set aside.
4Season chicken breast with salt and pepper, then sear in the same skillet over medium-high heat for 4–5 minutes per side until cooked through. Let cool, then dice into bite-sized pieces.
5Toss diced chicken with barbecue sauce to coat well.
6Place a pizza stone in the oven and preheat to 475°F for at least 15 minutes.
7Stretch dough on a piece of parchment paper into a 12-inch round. Arrange on the stone.
8Spread a thin layer of barbecue sauce on the dough, leaving a half-inch border.
9Scatter caramelized onions and BBQ chicken over the sauce. Top with cheddar and mozzarella, leaving some space at the edges.
10Bake for 12–14 minutes until crust is golden and cheese is melted and bubbling.
11Sprinkle with fresh cilantro and red pepper flakes if desired. Slice and serve hot.