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 pot over medium-high heat. Working in batches, brown beef chuck pieces and short ribs on all sides, approximately 3 to 4 minutes per batch. Remove browned 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, stirring occasionally, until the vegetables are softened and lightly charred.
04 - Drain the soaked chiles and transfer them to a blender. Add the sautéed onion, garlic, and tomatoes along with 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, rich 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. 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 fall-apart tender and easily shreddable.
06 - Remove the beef from the pot and shred it finely using two forks, discarding any large fat pieces or bones. Skim the bright orange fat from the surface of the consommé and reserve it in a small bowl for frying the tacos. Keep the shredded beef and the consommé warm separately.
07 - Heat a skillet or griddle over medium-high heat. Brush one side of each corn tortilla lightly with the reserved birria fat. Place tortillas fat-side down on the hot surface. While they begin to crisp, add a generous mound of shredded beef and a sprinkle of cheese onto one half of each tortilla. Fold each tortilla in half to form a taco and cook for 2 to 3 minutes per side until golden brown and crunchy.
08 - Transfer the crispy birria tacos to a platter. Top generously with finely diced white onion and chopped fresh cilantro. Serve immediately with lime wedges and small bowls of warm birria consommé on the side for dipping.