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 chuck 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 thoroughly to coat all meat. Bring to a simmer over medium heat, then cover and cook on low heat for 3 to 3.5 hours, until meat is fork-tender and easily shreds. Skim fat from the top and reserve for frying tacos.
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 well to coat in the consommé.
05 - Arrange chopped cilantro, diced white onion, and lime wedges in separate serving bowls.
06 - Heat a skillet over medium heat and add 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 on the skillet. Sprinkle cheese over half the tortilla, top with birria meat, and fold 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 alongside the consommé.