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, cover with hot water, and soak for 10 minutes to soften.
02 - In the same skillet, roast the quartered onion, garlic cloves, and halved tomatoes until lightly charred and softened, 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 and short ribs generously with salt and pepper in a large Dutch oven or stockpot. Pour in the blended chile sauce and remaining beef broth. Add the bay leaves and bring to a boil over high heat.
05 - Reduce heat to low, cover, and simmer for 2.5 to 3 hours until the beef is fork-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 dipping.
07 - Heat a skillet or griddle over medium heat. Briefly dip each corn tortilla into the reserved birria fat or a thin layer of consommé, then place on the hot surface.
08 - Sprinkle shredded cheese on one half of the tortilla, add a generous portion of shredded birria beef, and fold into a taco shape. Fry for 2-3 minutes per side until golden brown and crispy. Add neutral oil as needed.
09 - Serve the tacos immediately topped with chopped white onion and fresh cilantro. Accompany with lime wedges and small bowls of warm birria consommé for dipping.