Prepare Chiles:
Toast dried chiles in a dry skillet over medium heat for 1–2 minutes until fragrant (don’t burn). Soak them in hot water for 15 minutes to soften.
Sear the Meat:
Season beef generously with salt and pepper. In a large pot or Dutch oven, heat oil and sear meat on all sides until browned. Remove and set aside.
Make the Sauce:
In a blender, combine soaked chiles, onion, garlic, tomato, cumin, oregano, cloves, cinnamon stick (or ½ tsp ground cinnamon), and vinegar. Blend with 1 cup of beef broth until smooth.
Simmer:
Return meat to the pot. Pour sauce over the meat. Add remaining broth and bay leaves. Cover and simmer on low for 2½ to 3 hours, or until the meat is fall-apart tender.
Shred the Meat:
Remove meat from the pot, shred it with forks, then return to the pot and stir into the broth.
Serve:
As a Stew: Ladle birria into bowls with chopped onions, cilantro, and lime juice.
For Tacos: Dip corn tortillas into the consommé, fry lightly, then fill with shredded meat. Cook until crispy, and serve with consommé for dipping.