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 well.
02 - In a blender, combine softened chiles, onion, garlic, diced tomatoes, vinegar, oregano, cumin, paprika, cinnamon, cloves, salt, and black pepper. Blend until completely smooth.
03 - 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 thoroughly coated. Bring to a simmer over medium heat, then 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.
04 - Remove the beef from the pot and shred using two forks. Discard bones and bay leaf. Return shredded meat to the pot and stir to coat in the consommé.
05 - Arrange the chopped cilantro, diced onion, and lime wedges in separate serving bowls.
06 - 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, then 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 for 2-3 minutes per side, pressing gently, until crispy and golden brown. Repeat with remaining tortillas.
07 - Ladle consommé into small bowls for dipping. Serve tacos garnished with chopped onion, cilantro, and lime wedges, with consommé on the side.