01 - Toast dried guajillo, ancho, and pasilla chiles in a dry skillet over medium heat for 1-2 minutes until fragrant. Transfer to a bowl, cover with hot water, and soak for 10 minutes until softened.
02 - In the same skillet, roast quartered onion, garlic cloves, and halved Roma tomatoes until lightly charred and softened, about 5-7 minutes.
03 - Drain soaked chiles and transfer to a blender. Add roasted vegetables, apple cider vinegar, ground cumin, dried oregano, dried thyme, ground cinnamon, whole cloves, and 1 cup beef broth. Blend until completely smooth.
04 - Season beef chuck and short ribs generously with salt and pepper in a large Dutch oven or stockpot. Pour the blended chile mixture over the meat along with the remaining beef broth. Add bay leaves and stir to combine.
05 - Bring the mixture to a boil over high heat, then reduce to low. Cover and simmer for 2.5 to 3 hours until the beef is very tender and easily shreds with a fork. Skim excess fat from the surface and reserve for frying tacos.
06 - Remove beef from the pot and shred using two forks. Return the shredded meat to the pot to keep warm, or transfer to a separate container. Keep the consommé (cooking liquid) warm for dipping and tortilla preparation.
07 - Heat a skillet or griddle over medium heat. Briefly dip each corn tortilla in the top layer of birria consommé or reserved fat, coating both sides lightly.
08 - Place the dipped tortilla on the hot skillet. Sprinkle shredded cheese on one half, add a generous portion of shredded birria beef, then fold into a taco shape. Fry for 2-3 minutes per side until golden and crispy. Add neutral oil as needed. Repeat with remaining tortillas.
09 - Serve tacos immediately topped with finely diced white onion and chopped fresh cilantro. Accompany with lime wedges and small bowls of warm birria consommé for dipping.