01 - Toast dried guajillo, ancho, and pasilla chiles in a dry skillet over medium heat for 1-2 minutes until fragrant. Soak in hot water for 10 minutes until soft, then drain well.
02 - Combine softened chiles, quartered onion, garlic, diced tomatoes, vinegar, oregano, cumin, paprika, cinnamon, cloves, salt, and black pepper in a blender. Process until completely smooth.
03 - Place beef chunks and short ribs in a Dutch oven. Pour blended sauce over meat, add beef broth and bay leaf. Mix thoroughly to coat. Bring to simmer, cover, and cook on low for 3-3.5 hours until fork-tender. Skim fat from top and reserve for frying.
04 - Remove beef from pot, shred with two forks. Discard bones and bay leaf. Return shredded meat to pot and stir to coat in consommé.
05 - Arrange chopped cilantro, diced onion, and lime wedges in separate serving bowls.
06 - Heat skillet over medium heat with reserved fat or oil. Dip tortilla into 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.
07 - Ladle consommé into small bowls for dipping. Serve tacos garnished with onion, cilantro, and lime wedges alongside consommé.