1. In a large pot, add the beef chunks, dried guajillo chiles, dried ancho chiles, white onion, garlic, cumin, dried oregano, and beef broth.
2. Bring to a boil, then reduce heat and simmer for about 3 hours, or 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 contents of the pot until smooth to create the birria sauce.
5. Return the shredded beef to the pot and mix with the birria sauce. Season with salt and pepper to taste.
6. Heat the corn tortillas in a skillet until warm and pliable.
7. Serve the shredded beef on the warm tortillas, garnished with chopped cilantro, diced onion, and lime wedges.