Place rack in upper third of the oven and preheat oven to 425°F. Line a large baking sheet with parchment paper, or dust it with cornmeal or flour.
In a large bowl, whisk together the BBQ sauce and garlic powder. Add shredded chicken and toss to coat.
Place the dough on a lightly floured work surface and roll into an 11×14-inch rectangle. Gently transfer the rolled dough to a prepared baking sheet (you can also roll out the dough on floured parchment, then lift up the crust and paper together and set them on the baking sheet). Top with the BBQ chicken, leaving a 3/4 inch border uncovered around all sides.
Sprinkle on the mozzarella, cheddar cheese, and red onion. Bake for 15-18 minutes, until the crust is crisp and golden. Sprinkle with the green onion. Let cool a few minutes, then slice and serve.
Notes
TO STORE: Refrigerate BBQ chicken pizza in an airtight storage container for up to 3 days.
TO REHEAT: Warm up leftovers on a baking sheet in the oven at 350°F until the pizza is heated through.
TO FREEZE: Freeze pizza in an airtight storage container for up to 3 months. Reheat from frozen according to the instructions above.