01 - Place the 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 the toasted chiles to a large bowl and cover with hot water. Let them soak for 15 minutes until fully rehydrated and softened.
02 - Heat the oil in a large Dutch oven or heavy-bottomed pot over medium-high heat. Working in batches to avoid crowding, sear the beef chuck chunks and short ribs on all sides until deeply browned, approximately 3 to 4 minutes per side. Remove the browned meat and set aside on a plate.
03 - In the same pot with the rendered beef fat, add the quartered onion, garlic cloves, and quartered Roma tomatoes. Sauté over medium heat until the vegetables are softened and lightly caramelized, 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 chile 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, then pour in the remaining 3 cups of beef broth. Add the bay leaves and kosher salt. Stir thoroughly to combine.
06 - Bring the mixture to a gentle boil, then reduce the heat to low. Cover with a tight-fitting lid and let the birria simmer gently for approximately 3 hours, or until the beef is fork-tender and shreds effortlessly. Occasionally check the liquid level and skim any foam that rises to the surface. Once done, skim the fat layer from the top and reserve it in a small bowl for frying the tacos later.
07 - Transfer the braised beef to a large cutting board. Using two forks, shred the meat into fine strands, discarding any large pieces of fat or bone. Strain the remaining braising liquid through a fine-mesh sieve and reserve the consommé for serving alongside the tacos.
08 - Heat a large skillet or griddle over medium-high heat. Using a pastry brush, lightly coat one side of each corn tortilla with the reserved birria fat. Place the tortillas fat-side down on the hot surface. Working quickly, add a generous mound of shredded beef and a sprinkle of shredded cheese onto one half of each tortilla. Fold the tortilla over to form a taco and press gently with a spatula. Cook until the exterior is golden and crispy, about 2 to 3 minutes per side.
09 - Transfer the crispy birria tacos to a serving platter. Top generously with finely diced white onion and freshly chopped cilantro. Serve immediately with lime wedges and small bowls of warm birria consommé on the side for dipping.