01 - Toast dried chiles in dry skillet over medium heat 1-2 minutes until fragrant. Soak in hot water 10 minutes until soft, then drain. Blend softened chiles, onion, garlic, tomatoes, vinegar, oregano, cumin, paprika, cinnamon, cloves, salt, and pepper until smooth.
02 - Place beef chunks and short ribs in Dutch oven. Pour blended sauce over meat. Add beef broth and bay leaf. Mix well to coat. Bring to simmer over medium heat, then cover and cook on low 3-3.5 hours until fork-tender. Skim fat from top and reserve for frying.
03 - Remove beef from pot and shred with two forks. Discard bones and bay leaf. Return shredded meat to pot and stir to coat in consommé.
04 - Arrange chopped cilantro, diced onion, and lime wedges in separate serving bowls.
05 - Heat skillet with reserved fat or oil. Dip tortilla into top layer of birria consommé to coat. Place on skillet, sprinkle cheese over half, top with meat, fold tortilla. Cook 2-3 minutes per side until crispy and golden. Repeat with remaining tortillas.
06 - Ladle consommé into small bowls for dipping. Serve tacos garnished with onion, cilantro, and lime wedges alongside consommé.