1. In a large pot, add beef chunks and cover with water. Bring to a boil, then reduce heat and simmer for 10 minutes. Drain and set aside.
2. In the same pot, add beef broth, guajillo chiles, ancho chiles, onion, garlic, oregano, cumin, salt, and pepper. Bring to a boil, then reduce heat and simmer for 30 minutes.
3. Remove chiles, onion, and garlic from the pot and blend until smooth. Return the mixture to the pot.
4. Add the beef back to the pot and simmer on low heat for 3-4 hours, until the meat is tender and easily shredded.
5. Heat corn tortillas on a skillet until warm. Fill with shredded beef, and top with chopped cilantro, diced onion, and a squeeze of lime.