Preheat the oven to 475°F and line a baking sheet with parchment paper. Roll the pizza dough into a 12-inch circle or oval and place it on the prepared sheet.
Spread ½ cup of the BBQ sauce evenly over the dough, leaving a small border around the edge.
Scatter the shredded chicken across the sauce, arranging most of the pieces in two curved rows that fan outward to resemble bat wings.
Sprinkle the mozzarella and cheddar cheeses over the chicken and sauce. Scatter the sliced red onion on top.
Bake for 12 to 15 minutes until the crust is golden and the cheese is bubbling. Remove from the oven and drizzle with the remaining ¼ cup BBQ sauce.
Sprinkle the chopped cilantro over the hot pizza before slicing and serving.