Heat a cast iron skillet over medium high heat.
Toast the dried chiles quickly, being careful not to burn them.
Submerge the toasted chiles in hot water and allow to rehydrate for 20 minutes.
Next, using the same hot skillet, pan roast the tomatoes, onion, and garlic.
Transfer the vegetables and chiles to a blender and add 2 cups of water. Blend on high speed to puree the mixture.
Transfer the puree to a 6 quart crockpot, straining through a fine mesh strainer to catch any skins and seeds.
Pour one more cup of water into the blender and blend to release any extra sauce from the sides. Pour through the strainer into the crockpot.
Once the sauce has been strained, add the beef broth, cloves, cinnamon stick, cumin, mexican oregano, vinegar, coriander, bay leaves, salt, and pepper.
Turn the crockpot on low.
Using the same cast iron skillet, brown the short ribs and chuck roast on all sides.
Gently place the browned beef into the birria, being sure to cover all of the meat.
Cook on low for 8-10 hours.
Once the beef is falling off the bone tender, remove the beef pieces and allow to cool for 5 minutes.
Strain the birria broth to remove any fatty pieces, the cloves, cinnamon stick, and the bay leaves. Return the broth to the crock pot.
Shred the beef, removing any large fatty pieces and bones. Return the shredded beef to the broth.
Heat a large griddle to medium high heat and season with avocado oil.
Dip tortillas, one at a time, into the birria broth.
Cook the tortillas on the griddle for 1-2 minutes per side or until they are hot and slightly toasted.
Immediately add cheese and beef to the tortilla and fold over. Keep warm in a 100℉ oven while assembling each taco.
Once all of the tacos are finished cooking, top with onions, cilantro, and cotija cheese. Serve with a small bowl of birria broth and a lime wedge.