01 - In a dry skillet over medium heat, toast the dried guajillo, ancho, and pasilla chiles 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, 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 in a large Dutch oven. Pour the blended chile sauce over the meat and add remaining 5 cups beef broth. Add bay leaves and stir to combine.
05 - Bring mixture to a boil, then reduce heat to low. Cover and simmer for 2.5-3 hours until beef is fork-tender and shreds easily. Skim excess fat from surface and reserve for frying tacos.
06 - Remove beef from pot and shred using two forks. Return meat to the pot to keep warm in consommé, or transfer meat to a separate bowl and keep cooking liquid warm for serving.
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 dipped tortilla on hot skillet. Sprinkle cheese on one half, add generous portion of shredded beef, then fold tortilla into taco shape. Fry 2-3 minutes per side until golden and crispy. Add oil as needed.
09 - Serve tacos immediately topped with diced onion and cilantro. Accompany with lime wedges and small bowls of warm birria consommé for dipping.