1. Preheat oven to 200 degrees Fahrenheit
2. Combine chicken and one cup barbecue sauce in a nine-inch baking dish. Cover tightly and cook for five to six hours. Let cool, uncovered, for 30 minutes. Wearing gloves, roll each piece of chicken between your hands to shred thoroughly, so that no big chunks remain. (Alternatively, you can use two forks, but I find it easiest to break up all the bigger pieces with my hands.) Add the remaining cup of barbecue sauce and mix to combine.
3. Before frying pizza doughs, score an X through the center of each pizza round with a knife to prevent it from bubbling up.
4. Heat a pot with an inch or two of oil until hot, then fry each dough round for one to two minutes per side, until golden brown. Let cool on a wire rack. (If you don’t have a wire rack, you can crumple some tin foil and use that instead.)
5. To serve, top each pizza round with pulled chicken. Finish with desired sauces or toppings (I used garlic mayo, barbecue sauce, and Sriracha).
Tips: Make Ahead: Assuming you have a thousand other things to be on top of other than serving freshly fried pizza dough rounds, you can fry the doughs ahead of time and freeze. Reheat in a 350-degree-Fahrenheit oven for 15 minutes until hot and crispy. Pulled chicken can be made in advance as well; cover and reheat in a 350-degree-Fahrenheit oven.