01 - Place guajillo, ancho, and pasilla chiles in a dry skillet over medium heat. Toast for 1 to 2 minutes, turning occasionally, until fragrant but not burnt. Transfer to a heatproof bowl, cover with hot water, and soak for 15 minutes until pliable.
02 - Heat oil in a large Dutch oven or heavy pot over medium-high heat. Working in batches, brown the chuck roast chunks 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, 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 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 sauce through a fine-mesh strainer back into the Dutch oven, pressing with a spatula to extract as much liquid as possible. Return the seared beef to the pot. Pour in the remaining 3 cups of beef broth, add the bay leaves and salt, and stir to combine everything evenly.
06 - Cover the pot and reduce heat to low. Simmer gently for approximately 3 hours, checking occasionally, until the beef is fall-apart tender and shreds effortlessly with a fork. Skim the rendered fat from the surface and reserve it in a small bowl for frying the tacos.
07 - Remove the beef from the broth and place it on a cutting board. Using two forks, shred the meat into thin strands, discarding any large pieces of fat or bone. Strain the remaining birria consommé and keep it warm for dipping.
08 - 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 portion of shredded cheese onto one half of each tortilla. Fold in half to form tacos and cook for 2 to 3 minutes per side until golden brown and crispy.
09 - Transfer the crispy tacos to a serving 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.