01 - Toast the dried chiles in a dry skillet over medium heat for 1-2 minutes until fragrant. Soak them in hot water for 10 minutes until soft, then drain. In a blender, combine softened chiles, onion, garlic, tomatoes, vinegar, oregano, cumin, paprika, cinnamon, cloves, salt, and black pepper. Blend until smooth. Place the beef chunks and short ribs in a large Dutch oven or heavy pot. Pour the blended sauce over the meat. Add beef broth and bay leaf. Mix well to ensure meat is coated. Bring to a simmer over medium heat. Cover and cook on low for 3–3.5 hours, until the meat is fork-tender and easily shreds. Skim fat from the top and reserve for frying.
02 - Remove the beef from the pot and shred with two forks. Discard bones and bay leaf. Return shredded meat to the pot and stir to coat in consommé.
03 - In separate bowls, set out the chopped cilantro, diced onion, and lime wedges.
04 - Heat a skillet over medium heat and add a bit of reserved fat or oil. Dip a tortilla into the top layer of the birria consommé to coat in flavored fat. Place on the skillet. Sprinkle a layer of cheese over half of the tortilla, then top with birria meat. Fold the tortilla to close. Cook 2–3 minutes per side, pressing gently, until crispy and golden. Repeat with remaining tortillas.
05 - Ladle consommé into small bowls for dipping. Serve tacos garnished with chopped onion, cilantro, and lime wedges, with consommé on the side.