Remove the stems and seeds from the guajillo, ancho, and árbol chiles.
Place the dried chiles in a bowl and cover with hot water. Let them soak for 15 minutes, until softened.
Drain the chiles and transfer them to a blender.
Add tomatoes, onion, garlic, beef broth, apple cider vinegar, cumin, oregano, smoked paprika, cinnamon, cloves, salt, and black pepper.
Blend until the sauce is completely smooth. Add a little additional beef broth if needed.
Cut the chuck roast into large pieces and pat the beef dry.
Heat olive oil in a large skillet over medium-high heat. Sear the beef pieces for 2–3 minutes per side. This step is optional but adds extra flavor.
Place the seared beef and short ribs into the crockpot.
Pour the chile sauce over the beef and add the bay leaves.
Cover and cook on LOW for 8–9 hours or HIGH for 4–5 hours, until the beef is very tender and easily pulls apart with a fork.
Remove the beef from the crockpot and discard the bones and large pieces of excess fat.
Shred the beef using two forks.
Return the shredded beef to the crockpot and stir it into the broth.
Let the shredded beef sit in the broth for another 10–15 minutes.
Serve the birria with warm tortillas, onion, cilantro, lime, and your favorite toppings.
For birria tacos, lightly dip corn tortillas into the flavorful fat on top of the broth.
Place the tortillas in a hot skillet, add cheese and shredded beef, fold, and cook for 2–3 minutes per side, until crispy and golden.
Serve the crispy tacos with small bowls of the birria broth for dipping.