Preheat the oven. Heat your oven to 475°F (245°C). If you have a pizza stone or steel, place it in the oven while it preheats for at least 30 minutes. A hot surface gives you a crisp, blistered crust.
Prep the chicken. Toss the cooked chicken with 2–3 tablespoons of barbecue sauce, just enough to lightly coat.
Season with a pinch of salt and pepper. This keeps the chicken moist and flavorful.
Stretch the dough. Lightly flour your counter. Press and stretch the dough into a 12–14 inch round (or rectangle if using a sheet pan).
Avoid overworking it; let it rest a minute if it resists. Transfer to a cornmeal-dusted pizza peel or an oiled baking sheet.
Sauce the base. Spread about 1/3 to 1/2 cup barbecue sauce over the dough, leaving a small border. Don’t drown it—too much sauce makes the crust soggy.
Add cheese and toppings. Sprinkle most of the mozzarella over the sauce.
Add the smoked gouda or cheddar if using. Scatter the sauced chicken evenly, then add the red onion slices. Finish with the remaining mozzarella for good melt and coverage.
Bake. Slide the pizza onto the hot stone or place the baking sheet in the oven.
Bake 10–14 minutes, until the crust is golden and the cheese is bubbling with browned spots.
Finish and rest. Remove from the oven. Drizzle a small ribbon of barbecue sauce over the top if you like. Let the pizza rest 2–3 minutes, then sprinkle with chopped cilantro and a pinch of red pepper flakes if desired.
Slice and serve. Cut into 6–8 slices.
Serve hot while the cheese is stretchy and the crust is crisp.