Begin by making the pizza dough: In your bread machine, add all the ingredients in the order suggested by your bread machine. Select the dough cycle, and let it run the full cycle.
While the dough rises, bake the chicken: Preheat the oven to 450 degrees. Place the breasts in a small baking dish and top with the garlic, butter, oil, salt and pepper. Bake for twenty minutes. With a fork, crush the garlic and rub it all over the chicken. Cut the chicken in bite size pieces, and set aside..
Next, make the Red Barbecue Sauce: In a three quart saucepan, melt the butter and cook the onion and garlic until they're softened, on low heat, for about five minutes. Add the rest of the ingredients and simmer for 15 minutes. Stir in the chopped chicken.
Next, make the White Barbecue Sauce: Simply mix the ingredients together in a small bowl, and refrigerate.
When the dough cycle ends, preheat the oven to 425 degrees, and add the pizza stones if you're using them. On a floured board, divide the dough into two balls.
Line your pizza peels or baking sheets with parchment paper, and using your fingers press each ball of dough into a 12 inch circle on the papers. Brush each circle with olive oil, and cover loosely with plastic wrap. Let rise for thirty minutes. Then bake for 15 minutes either on the pizza stones or on baking sheets.
Remove the pizzas from the oven using the pizza peels. Spread the pizza with the Red Barbecue Sauce and chicken, and then add the cheeses, red onion, and tomato. Bake for ten more minutes. Before serving, drizzle with some of the White Barbecue Sauce and the cilantro.