01 - Heat a dry skillet over medium heat. Toast guajillo, ancho, and pasilla chiles for 1-2 minutes until fragrant. Transfer to a bowl, cover with hot water, and soak for 10 minutes.
02 - In the same skillet, roast quartered onion, garlic cloves, and halved tomatoes until lightly charred on all sides.
03 - Drain soaked chiles and transfer to a blender. Add charred vegetables, apple cider vinegar, cumin, oregano, thyme, cinnamon, cloves, and 1 cup beef broth. Blend until completely smooth.
04 - Season beef chuck and short ribs generously with salt and pepper. Place in a large Dutch oven or stockpot. Pour in blended chile mixture and remaining 5 cups beef broth. Add bay leaves. Bring to a boil, then reduce heat to low. Cover and simmer for 2.5 to 3 hours until meat shreds easily.
05 - Remove beef from the pot, reserving all cooking liquid. Shred meat using two forks. Skim excess fat from the consommé and reserve separately for frying.
06 - Heat a skillet or griddle over medium heat. Lightly dip each corn tortilla in the reserved fat or top layer of consommé. Place on the hot skillet.
07 - Sprinkle cheese on one half of the tortilla. Add a generous portion of shredded birria beef. Fold tortilla into a taco shape. Fry for 2-3 minutes per side until golden and crispy. Add neutral oil as needed. Repeat with remaining tortillas.
08 - Serve tacos immediately topped with diced onion and cilantro. Accompany with lime wedges and small bowls of warm birria consommé for dipping.