Soak the dried chiles in hot water until softened, about 20 minutes. Blend them with onion, garlic, vinegar, and spices until smooth.
In a large pot, sear the beef chunks and short ribs until browned on all sides.
Pour the blended chile sauce over the meat and add beef broth, bay leaves, and cinnamon stick. Bring to a boil, then lower heat and simmer for 2.5 to 3 hours until the meat is tender and shreds easily.
Remove the meat from the pot, shred it, and set aside. Strain the broth if needed.
Heat a skillet over medium heat. Dip each tortilla in the birria broth, place it on the skillet, add cheese and shredded beef, then fold it in half.
Cook until crispy on both sides and cheese is melted. Serve with chopped onions, cilantro, and lime wedges.