Wipe the guajillo, ancho and chile de arbol clean with a damp cloth, then toast them in a dry Dutch oven over medium heat for about 30 seconds per side, until they smell fragrant and puff slightly. Pour in 2 cups of the beef broth, cover, and let the chiles soak off the heat for 15 minutes, until soft enough to pierce with a fork.
Season the chuck roast pieces all over with the salt and pepper. Heat the oil in the same Dutch oven over medium high, then sear the beef in batches for 3 to 4 minutes per side, until a deep brown crust forms on every cut surface. Transfer the seared beef to a 6 quart slow cooker insert.
Pour the soaked chiles and their soaking liquid into a blender. Add the chopped onion, garlic, diced tomatoes, vinegar, tomato paste, cumin and oregano, then blend on high for about 1 minute, until the sauce is smooth and brick red with no visible chile skins.
Pour the blended sauce over the seared beef in the slow cooker. Add the cinnamon stick, bay leaves and the remaining 2 cups of beef broth, then stir once to settle the beef under the liquid.
Cover and cook on low for 8 hours, or on high for 4 to 5 hours, until a fork slides into the beef with no resistance and the meat is ready to fall apart.
Lift the beef onto a cutting board and let it rest for 10 minutes, this keeps the shreds from drying out. Shred the beef into bite sized pieces with two forks, then discard the cinnamon stick and bay leaves from the broth.
Skim about 1/2 cup of the fat pooled on the surface of the broth into a small bowl, this is what you will dip the tortillas in. Return the shredded beef to the broth to keep it moist, then ladle 3 cups of the broth into small cups for dipping.
Dip one side of a corn tortilla into the reserved fat, then lay it fat side down in a hot skillet over medium heat. Scatter 2 tablespoons of the shredded cheese and a small handful of the shredded beef over one half of the tortilla.
Fold the empty half of the tortilla over the filling and press gently. Cook for 2 to 3 minutes per side, flipping once, until the tortilla is crisp and spotted brown and the cheese has melted inside.
Transfer the finished tacos to a platter and repeat with the remaining tortillas, cheese and beef. Serve immediately with the diced onion, chopped cilantro, lime wedges and the small cups of broth for dipping.
Good to Know
Do not skip skimming the fat before frying: that spoonful is what turns a plain tortilla into the crisp, deep red shell birria is known for.