Toast and Soak Chiles: Heat a skillet and toast the guajillo and ancho chiles for 30 seconds. Soak them in hot water for 15-20 minutes to rehydrate.
Prepare Beef: Season beef chunks with salt and pepper. Heat oil in a large pot, sear the beef until browned on all sides.
Make the Sauce: Blend the soaked chiles, garlic, onion, tomatoes, cinnamon, oregano, and vinegar until smooth.
Cook: Add the sauce, beef broth, and bay leaves to the pot. Bring to a boil, then reduce the heat and simmer for 2-3 hours or until beef is tender.
Shred Beef: Remove beef, shred it using two forks, and return it to the pot. Adjust seasoning with salt and pepper.
Serve: Serve with tortillas, fresh cilantro, onions, and lime. Optionally, serve with a bowl of the consomé for dipping.