1. In a large pot, combine beef, beef broth, guajillo chiles, ancho chiles, onion, garlic, oregano, cumin, salt, and black pepper. Bring to a boil.
2. Reduce heat and simmer for about 3 hours, until the beef is tender and shreds easily.
3. Remove the beef from the pot and shred it using two forks.
4. Blend the remaining broth and solids in the pot until smooth. Return the shredded beef to the pot and mix well.
5. Heat the corn tortillas in a skillet until warm and slightly crispy.
6. Serve the shredded beef on the tortillas, topped with chopped cilantro, diced onions, and lime wedges.