01 - Heat a dry skillet over medium heat. Toast the 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. Pour the blended chile sauce over the meat and add the remaining beef broth and bay leaves. Bring to a boil, then reduce heat to low. Cover and simmer for 2.5 to 3 hours until beef shreds easily.
05 - Remove the beef from the pot and shred using two forks. Skim any excess fat from the surface and reserve for frying. Keep the consommé warm.
06 - Heat a skillet or griddle over medium heat. Briefly dip each tortilla in the reserved fat or top layer of consommé. Place on the hot skillet, sprinkle cheese on one half, add shredded beef, and fold into a taco. Fry for 2-3 minutes per side until golden and crispy. Repeat with remaining tortillas, adding oil as needed.
07 - Serve the tacos immediately, topped with chopped onion and cilantro. Accompany with lime wedges and small bowls of warm birria consommé for dipping.