In a large pot, bring the ham hock, carrots, garlic, onion, celery, bay leaf and water to a boil. Cover partially and simmer over low heat for 2 hours. Strain, return to the pot and boil until reduced to 10 cups, 10 minutes; skim.
Add the hominy, black beans, red bell pepper and ancho and season with salt and pepper. Simmer until the bell pepper is tender, about 6 minutes. Add the shrimp and cook until pink. Add the lime juice. Ladle into bowls, garnish with the avocado and cilantro and serve.
Notes: One Serving 285 calories, 4 gm total fat, 2 gm saturated fat, 32 gm carb.