In a Dutch oven, heat vegetable oil over medium-high heat. Brown the chuck roast and short ribs on all sides.

Remove the meat and set aside. In the same pot, add chopped onion and garlic, sauté until softened.

In a blender, combine the guajillo and ancho chiles with beef broth, cumin, oregano, thyme, black pepper, and salt. Blend until smooth.

Return the meat to the pot, pour the blended sauce over it, and bring to a simmer.

Cover and cook on low heat for about 3-4 hours, until the meat is tender and easily shredded.

Once the meat is cooked, shred it using two forks and mix it with the broth.

In a skillet, heat the corn tortillas until warm. Fill each tortilla with shredded birria meat.

Top with chopped cilantro and onion. Serve with lime wedges and the reserved broth for dipping.