How to Make It
In a large stockpot, cover the turkey carcass, onion, carrot, celery and bay leaf with 16 cups of water and bring to a boil over moderately high heat. Simmer the turkey stock over moderate heat until the broth is flavorful, about 2 hours. Strain the broth through a coarse sieve into a large heatproof bowl.
Return the broth to the stockpot. Add the hominy, tomatoes, garlic and jalapeño and cook over moderately high heat until the broth is reduced to 6 cups, about 30 minutes. Add the shredded turkey and chopped cilantro and simmer until the stew is heated through. Season the posole with salt, ladle into deep bowls and serve with the avocado chunks, shredded Monterey Jack cheese and warm tortillas.