Prepare the dough by mixing warm water, yeast, olive oil, salt, and flour in a large mixing bowl using an electric mixer with a dough hook. Divide dough into 8 equal balls and let rise on a lightly oiled baking sheet, covered with a damp towel, for 1 to 1 1/2 hours.
Preheat your grill for grilling chicken breasts
Season chicken breasts with Sweet Brown Sugar Rub and grill until internal temperature reaches 165F (about 7-8 minutes per side). Let rest for 4-5 minutes before slicing thinly.
Arrange shredded cheese, sliced chicken, sliced red onions, BBQ sauce, and cilantro on a cutting board near your prep station.
Coat hands with olive oil, shape dough balls into disks with even thickness.
Layer BBQ sauce, mozzarella, chicken, red onions, and cheddar cheese onto the pizza dough
Place BBQ pizza in the pizza oven and rotate often to ensure evenly cooked crust
Transfer pizza to a cutting board, drizzle with more BBQ sauce if desired, and serve. Repeat the process for the remaining dough balls.