Prepare the Chiles:
In a dry skillet, toast the guajillo, ancho, and pasilla chiles over medium heat for 2-3 minutes until fragrant. Remove them from the heat and soak them in a bowl of hot water for 20 minutes.

Make the Sauce:
Blend the soaked chiles, garlic, diced tomatoes, cumin, oregano, cinnamon, cloves, apple cider vinegar, brown sugar, and beef broth in a blender until smooth. Taste and adjust seasoning with salt and pepper.

Brown the Beef:
Heat vegetable oil in a large Dutch oven or heavy-bottomed pot over medium-high heat. Season the beef with salt and pepper, and sear it in batches until browned on all sides, about 3-4 minutes per side. Remove and set aside.

Cook the Birria:
Pour the blended sauce over the beef in the pot, ensuring the beef is covered with the sauce. Add more broth if needed. Bring the liquid to a simmer, then cover and reduce the heat to low. Let the meat cook for 3-4 hours, or until fork-tender. (Alternatively, use a slow cooker on low for 6-8 hours or an Instant Pot for 45 minutes.)

Shred the Meat:
Once the meat is tender, remove it from the pot and shred it using two forks. Discard any bones if using cuts like oxtail or shank. Return the shredded beef to the broth and mix well.

Assemble the Tacos:
Heat tortillas in a pan until warm. Dip each tortilla into the consomé to soak it slightly, then cook it in a hot skillet until crispy and golden. Add a generous amount of shredded beef to the tortilla and fold it in half.

Serve and Garnish:
Top each taco with cilantro, chopped onion, and a squeeze of lime. Serve with a bowl of consomé for dipping.