In a skillet, dry-toast the guajillo and ancho chiles over medium heat until fragrant (about 2–3 minutes). Then, soak the chiles in hot water for about 20 minutes until softened.

While the chiles are soaking, blend the softened chiles with beef broth, chopped onion, garlic, cumin, oregano, salt, and pepper until smooth.

Cut the beef chuck roast into large chunks. Combine the beef, short ribs, and marinade in a large bowl or a zip-top bag. Let it marinate for at least 1 hour (or overnight for maximum flavor).

In a large pot, heat some oil over medium heat. Add the marinated beef and sear it on all sides. Pour in any remaining marinade and bring the mixture to a gentle simmer.

Cover and cook on low heat for about 2–3 hours, or until the meat is tender and shreds easily with a fork.

While the meat is cooking, heat a skillet over medium heat. Lightly grill the corn tortillas until warm and pliable.

Use a fork to shred the beef from the pot. Fill the tortillas with shredded beef and top with chopped onions and cilantro. Serve with lime wedges on the side.