01 - Toast the dried guajillo, ancho, and pasilla 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 thoroughly.
02 - Combine softened chiles, quartered onion, garlic, diced tomatoes, vinegar, oregano, cumin, paprika, cinnamon, cloves, salt, and black pepper in a blender. Blend until completely smooth.
03 - Place beef chunks and short ribs in a Dutch oven or heavy pot. Pour the blended sauce over the meat. Add beef broth and bay leaf. Mix well to coat all meat. Bring to a simmer over medium heat, then cover and reduce to low.
04 - Cook covered on low heat for 3 to 3.5 hours until meat is fork-tender and easily shreds. Skim excess fat from the top and reserve for frying tacos.
05 - Remove beef from the pot, discarding bones and bay leaf. Shred meat using two forks. Return shredded meat to the pot and stir to coat thoroughly in the consommé.
06 - Arrange chopped cilantro, diced onion, and lime wedges in separate bowls for serving.
07 - Heat a skillet over medium heat with reserved fat or oil. Dip a tortilla into the top layer of birria consommé to coat in flavored fat, then place on skillet. Sprinkle cheese over half the tortilla, top with birria meat, and fold to close. Cook 2-3 minutes per side, pressing gently, until crispy and golden. Repeat with remaining tortillas.
08 - Ladle consommé into small bowls for dipping. Serve tacos garnished with chopped onion, cilantro, and lime wedges alongside the consommé.