01 - Place guajillo, ancho, and pasilla chiles in a dry skillet over medium heat. Toast 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 oil in a large Dutch oven or heavy pot over medium-high heat. Working in batches, brown the beef chuck pieces and short ribs on all sides, approximately 3 to 4 minutes per batch. Remove the seared meat and set aside on a plate.
03 - In the same pot, add the quartered onion, garlic cloves, and quartered Roma tomatoes. Sauté over medium heat for about 5 minutes until the vegetables are softened and lightly charred. Remove from the pot and set aside.
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 beef broth. Blend on high until completely smooth.
05 - Pour the blended chile sauce through a fine-mesh strainer back into the Dutch oven, pressing with a spatula to extract all liquid. Return the seared beef to the pot, then add the remaining 3 cups of beef broth, bay leaves, and salt. Stir to combine. Cover tightly and simmer gently over low heat for approximately 3 hours, until the beef is fall-apart tender and easily shreddable. Skim the rendered fat from the surface and reserve it separately for frying the tacos.
06 - Remove the beef from the braising liquid and place it in a large bowl. Using two forks, shred the meat into fine strands. Strain the remaining consommé through a fine-mesh sieve and keep warm for serving alongside the tacos.
07 - Heat a skillet or griddle over medium-high heat. Lightly brush one side of each corn tortilla with the reserved birria fat. Place tortillas fat-side down on the hot surface. Add a generous mound of shredded beef and a portion of shredded cheese onto one half of each tortilla. Fold in half to form tacos and press gently with a spatula. Cook for 2 to 3 minutes per side until the tortillas are deeply golden and crisp and the cheese has melted.
08 - Transfer the crispy tacos to a platter and garnish generously with finely diced white onion and chopped fresh cilantro. Serve immediately with lime wedges and small bowls of hot birria consommé for dipping.