Place the beef shank in a large heavy stock pot. Add enough cold water to cover the beef shank completely. Add the onion, carrot, celery, garlic cloves, and bay leaves. Season with 2 tablespoons of salt and 1 tablespoon of peppercorns. Bring to a boil, cover, and reduce heat to a simmer. Cook until the meat is fully cooked and tender, about 2 hours. Be sure to constantly skim the fat from the surface of the liquid while cooking.
Remove the meat from the pot and let cool. Strain the liquid and return to the pot. Add the hominy and bring to a boil. Lower the heat to a simmer. Season with salt and pepper, to taste.
Using a fork, shred the meat into thin pieces and return to the pot adding 1 cup of water, if necessary. Season with salt and pepper, to taste. Simmer for 5 minutes.
Serve hot, garnished with cabbage, radishes, lime wedges, dried oregano, tostadas, and Pasilla-Guajillo Salsa, if using.
Soak the chiles and garlic cloves in warm water until the chiles are soft. Place the chiles, garlic, and water in a blender and process until smooth. Season with salt and pepper, to taste. Serve with Beef Pozole as a garnish.
Stir the Pasilla-Guajillo Salsa directly into the pozole if you want it to be spicy and red in color.
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