01 - Warm the guajillo, ancho, and pasilla chiles in a dry skillet over medium heat for 1 to 2 minutes, turning occasionally, until fragrant and pliable. Transfer to a heatproof bowl, cover with hot water, and soak for 15 minutes until fully softened.
02 - Heat the oil in a large Dutch oven or heavy pot over medium-high heat. Working in batches, brown the chuck roast pieces and short ribs on all sides, approximately 3 to 4 minutes per batch. Transfer the seared meat to a plate and set aside.
03 - In the same pot, reduce heat to medium. Add the quartered onion, garlic cloves, and quartered Roma tomatoes. Sauté until the vegetables are softened and lightly charred, about 5 minutes.
04 - Drain the soaked chiles and transfer them to a blender. Add the sautéed onion, garlic, and tomatoes along with the cinnamon stick, black peppercorns, cumin seeds, coriander seeds, whole cloves, dried oregano, dried thyme, apple cider vinegar, and 1 cup of the beef broth. Blend on high until a smooth, thick paste forms.
05 - Pour the blended sauce through a fine-mesh strainer back into the pot, pressing with a spatula to extract all liquid. Return the seared beef to the pot and add the remaining 3 cups of beef broth, bay leaves, and salt. Stir to combine, bring to a gentle simmer, then cover and cook over low heat for approximately 3 hours, until the beef is fork-tender and shreds effortlessly. Skim the rendered fat from the surface and reserve it for frying the tacos.
06 - Remove the beef from the braising liquid and shred it thoroughly using two forks, discarding any large pieces of connective tissue. Strain the remaining consommé and keep it warm for serving alongside the tacos.
07 - Heat a skillet or griddle over medium-high heat. Brush one side of each corn tortilla with the reserved birria fat. Place the tortillas fat-side down on the hot surface and cook for about 30 seconds until lightly golden. Add a generous portion of shredded beef and a sprinkle of cheese to one half of each tortilla, fold over to form a taco, and continue cooking for 2 to 3 minutes per side until the tortilla is deeply golden and crispy and the cheese has melted.
08 - Transfer the crispy tacos to a platter and top generously with finely diced white onion and chopped fresh cilantro. Serve immediately with lime wedges and small bowls of warm birria consommé for dipping.