01 - In a dry skillet over medium heat, toast the dried guajillo, ancho, and pasilla chiles for 1-2 minutes until fragrant. Place chiles in a bowl and cover with hot water. Soak for 10 minutes to soften.
02 - In the same skillet, roast the quartered onion, garlic cloves, and halved Roma tomatoes until lightly charred and softened, about 5-7 minutes.
03 - Transfer the soaked chiles (drained), roasted vegetables, apple cider vinegar, cumin, oregano, thyme, cinnamon, cloves, and 1 cup beef broth to a blender. Blend until completely smooth.
04 - In a large Dutch oven or stockpot, season the beef chuck and short ribs generously with salt and pepper. Pour in the blended chile mixture and remaining beef broth. Add the bay leaves.
05 - Bring the mixture to a boil, then reduce heat to low. Cover and simmer for 2.5 to 3 hours, or until the beef is very tender and shreds easily. Skim excess fat from the surface if desired and reserve for frying tacos.
06 - Remove the beef from the pot and shred using two forks. Reserve the consommé (cooking liquid) and keep warm for serving.
07 - Heat a skillet or griddle over medium heat. Have the shredded beef, cheese, and reserved birria fat or oil ready.
08 - Dip each tortilla briefly in the top layer of birria consommé or reserved fat, then place on the hot skillet. Sprinkle cheese on one half of the tortilla, add a generous amount of shredded birria beef, then fold into a taco shape. Fry for 2-3 minutes per side until golden and crispy. Repeat with remaining tortillas, adding more oil to the skillet as needed.
09 - Serve tacos hot, topped with chopped onion and cilantro. Accompany with lime wedges and a bowl of warm birria consommé for dipping.