In a large bowl, add warm water, yeast, and ½ cup flour. Whisk and set aside for 30 minutes.
After half an hour, whisk in cold water, oil, sugar, and salt. Add remaining flour and knead until a dough forms. Cover bowl with a towel and let the dough rise for 1 hour.
Preheat oven to 375°F. Add chicken breast to a small baking pan, and cover with 2 tbsp barbecue sauce. Sprinkle with salt and pepper.
Bake 20-25 min. Remove from oven and cool.
Shred the chicken breast with a fork.
Preheat oven to 500°F.
Cover a baking sheet with parchment paper and lightly dust with flour. Once the dough has risen, divide it in half (you can make two pizzas, or cover the other half and freeze it). With a rolling pin, roll out the dough on a floured surface to ¼-inch thickness. Place on baking sheet.
Spread ⅓ cup barbecue sauce over the dough, avoiding the edges. Sprinkle with cheese. Add shredded chicken and red onion slices.
Bake 10 minutes.
Remove pizza from oven and top with avocado pieces and chopped cilantro.