01 - In a dry skillet over medium heat, toast the dried guajillo, ancho, and pasilla chiles for 1-2 minutes until fragrant. Transfer to a bowl, cover with hot water, and soak for 15 minutes until softened.
02 - In the same skillet, roast the quartered onion, garlic cloves, and halved Roma tomatoes until slightly charred, about 5 minutes.
03 - Drain the soaked chiles and combine with the roasted vegetables, apple cider vinegar, oregano, thyme, cumin seeds, peppercorns, cloves, and 1 cup of beef broth in a blender. Blend until completely smooth.
04 - Heat vegetable oil in a large Dutch oven over medium-high heat. Sear the beef chuck chunks and short ribs on all sides until deeply browned.
05 - Pour the blended sauce over the browned beef. Add the remaining beef broth, bay leaves, cinnamon stick, and salt. Bring to a boil, then reduce heat to low. Cover and simmer for 2.5-3 hours until the meat is fork-tender and easily shreds.
06 - Remove the beef from the pot and shred using two forks, discarding bones and excess fat. Skim any excess fat from the birria consommé, reserving a small amount for frying the tortillas.
07 - Preheat oven to 375°F. Dip each corn tortilla in the warm birria consommé, then fry briefly in a hot skillet with a little reserved fat until pliable, about 10-15 seconds per side.
08 - Fill each tortilla with shredded birria and a sprinkle of cheese. Roll up tightly and place seam-side down in a baking dish.
09 - Pour extra birria consommé over the enchiladas and top with remaining cheese. Bake for 10-15 minutes until cheese is melted and bubbly.
10 - Serve hot, garnished with diced white onion, chopped fresh cilantro, and lime wedges on the side.