Take the dough ball from the refrigerator and bring to room temperature. While the dough is warming up, start the grill and set it for high heat/two-zone grilling (400-500) degrees on 1 side and no heat on the other. Spread your cornmeal on a cutting board. Place the dough on the cutting board and roll out to the shape of a pizza crust. Brush the pizza crust with 1 tablespoon of olive oil from edge to edge and lightly sprinkle with barbecue rub.
Place the crust on the hot side of the grill, oiled side down. Oil the other side immediately, and add the rub. When the dough has bubbled all across the top, check the underside for browning. Once browned evenly, remove from the grill, place on a clean cutting board, browned side up. Spread the barbecue sauce like pizza sauce over the browned crust.
Put a good layer of cheese and pulled pork over the sauce. Return to the hot side of the grill and close the lid. Once the bottom is browned, slide the crust over to the side with no heat and close the lid to heat the pulled pork for 6-8 minutes. Once the toppings are warm and melted and the bottom browned, remove from the grill, slice, and serve.