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 softened.
02 - Heat oil in a large Dutch oven or heavy-bottomed pot over medium-high heat. Working in batches, brown the beef chuck 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, reduce heat to medium. Add the quartered onion, garlic cloves, and quartered Roma tomatoes. Sauté 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 a smooth, deep red sauce forms.
05 - Pour the blended 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 and add the remaining 3 cups of beef broth, bay leaves, and salt. Stir well to combine. Bring to a gentle boil, then reduce heat to low. Cover and simmer for approximately 3 hours, until the beef is fork-tender and shreds easily.
06 - Remove the beef from the pot and shred using two forks, discarding any large pieces of fat or bone. Skim the layer of fat from the surface of the consommé and reserve it in a small bowl for frying the tortillas. Keep the shredded beef warm in a portion of the consommé.
07 - Heat a skillet or griddle over medium-high heat. 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 sprinkle of cheese onto one half of each tortilla. Fold in half to form tacos and cook for 2 to 3 minutes per side, pressing gently, until the tortillas are golden brown and crispy.
08 - Transfer crispy tacos to a platter. Top generously with finely diced white onion and chopped fresh cilantro. Serve immediately with lime wedges and small bowls of hot birria consommé on the side for dipping.