Break down chickens to get 4 breasts on the bone (with skin) and 4 leg-thigh pieces. Trim all fat and skin from the carcasses and hack into small pieces.
In a small bowl, combine chili powder, ground cumin, fennel pollen, white pepper, and fine salt. Rub all over chicken breasts, cover and keep refrigerated.
Preheat an outdoor grill for indirect grilling. Season chicken legs with salt and pepper, wrap in aluminum foil to form a pouch. Grill away from the heat source until chicken is very tender, about 1 hour.
Place the chicken bones, dried mushrooms, carrots, celery, onion and salt in cheesecloth and tie off with twine. Add beer and water to stock pot and toss in tied up bones. Bring to a boil and lower to a simmer. Simmer for 2 hours. Remove tied up bones.
After the legs have cooked for 1 hour, remove from grill. Discard skin and bones, shred chicken meat and set aside. Place dry rubbed chicken breast on grill skin side down over direct heat. Grill chicken, turning once, until cooked through about 5 to 6 minutes per side. Meanwhile, in a saucepan, heat Barbecue Sauce to simmering. Stir in leg meat.
When the dish is 5 minutes away from finished, measure out 4 cups hot stock into a clean saucepan. Return to simmer, add white rice, cover and remove from heat. Let sit 5 minutes, then fluff with a fork.
Slice chicken breast, serve over rice with leg meat and Corn and Black Bean Salsa.
Combine all ingredients in a large bowl.
Black Bean and Corn Salsa:
In a mixing bowl, toss all of the ingredients together and let sit for 1 hour.
A viewer or guest of the show, who may not be a professional cook, provided this recipe. It has not been tested for home use.