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, onion, garlic, diced tomatoes, vinegar, oregano, cumin, paprika, cinnamon, cloves, salt, and black pepper in a blender. Blend until completely smooth, scraping down sides as needed.
03 - Place beef chuck chunks and short ribs in a large Dutch oven or heavy pot. Pour the blended marinade over the meat, add beef broth and bay leaf. Mix thoroughly to ensure all meat pieces are evenly coated.
04 - Bring the mixture to a simmer over medium heat. Cover tightly and reduce heat to low. Cook for 3 to 3.5 hours until meat is fork-tender and easily shreds apart. Skim the fat layer from the top and reserve for frying tacos.
05 - Remove beef from the pot, discard bones and bay leaf. Shred the meat using two forks. Return shredded meat to the pot and stir well to coat in the flavorful consommé.
06 - Arrange chopped cilantro, diced white onion, and lime wedges in separate serving bowls. Keep consommé warm for dipping.
07 - Heat a skillet over medium heat with a small amount of reserved fat or oil. Dip a tortilla into the top layer of birria consommé to coat in flavored fat, then place in skillet. Sprinkle cheese over half the tortilla, add birria meat, and fold to close.
08 - Cook tacos for 2-3 minutes per side, pressing gently with a spatula, until tortilla is crispy and golden brown with melted cheese. Repeat with remaining tortillas, adding more fat as needed.
09 - Ladle consommé into small bowls for dipping. Serve tacos immediately, garnished with chopped onion, cilantro, and lime wedges on the side, with warm consommé for dipping.