01 - Toast the 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, onion, garlic, diced tomatoes, vinegar, oregano, cumin, paprika, cinnamon, cloves, salt, and black pepper in a blender. Process until completely smooth.
03 - Place beef chuck and short ribs in a Dutch oven. Pour blended sauce over meat, add beef broth and bay leaf. Bring to simmer over medium heat, then cover and reduce to low. Cook for 3 to 3.5 hours until meat is fork-tender and shreds easily. Skim fat from surface and reserve for frying.
04 - Remove beef from pot and shred using two forks. Discard bones and bay leaf. Return shredded meat to pot and stir thoroughly 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, then place on skillet. Sprinkle cheese over half the tortilla, top with meat, and fold to close. Cook 2-3 minutes per side, pressing gently, 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.