In a large pot, combine beef chuck roast, lamb shank, and water. Bring to a boil, then reduce heat and simmer for 2 hours.

In a separate pot, soak guajillo and ancho chiles in hot water for 15 minutes until soft.

Blend soaked chiles with onion, garlic, cumin, oregano, black pepper, and salt until smooth.

Add the blended mixture to the pot with meat, along with beef broth. Simmer for an additional 1.5 hours until meat is tender.

Remove meat from the pot, shred it, and return it to the broth. Adjust seasoning if necessary.

Heat a skillet over medium heat. Dip tortillas in the birria broth, then place them on the skillet.

Add shredded meat to one half of the tortilla, sprinkle with cilantro and onion, then fold the tortilla over.

Cook until crispy on both sides, about 2-3 minutes per side.

Serve tacos with lime wedges and a small bowl of birria broth for dipping.