01 - Heat a dry skillet over medium heat. Toast the dried guajillo, ancho, and pasilla chiles for 1-2 minutes until fragrant. Transfer to 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 tomatoes until lightly charred, about 5-7 minutes.
03 - Drain the soaked chiles and transfer to a blender. Add the roasted vegetables, apple cider vinegar, cumin, oregano, thyme, cinnamon, cloves, and 1 cup of beef broth. Blend until completely smooth.
04 - Season the beef chuck roast and short ribs generously with salt and pepper in a large Dutch oven or stockpot. Pour the blended chile sauce over the meat and add the remaining beef broth. Tuck in the bay leaves.
05 - Bring the mixture to a boil, then reduce heat to low. Cover and simmer for 2.5 to 3 hours until the beef is very tender and shreds easily. Skim excess fat from the surface and reserve for frying tacos.
06 - Remove the beef from the pot and shred using two forks. Strain the consommé if desired and keep warm for serving.
07 - Heat a skillet or griddle over medium heat. Briefly dip each tortilla in the top layer of birria consommé or reserved fat.
08 - Place the dipped tortilla on the hot skillet. Sprinkle cheese on one half, 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. Add more oil as needed.
09 - Serve tacos immediately topped with chopped onion and cilantro. Accompany with lime wedges and warm birria consommé for dipping.