01 - In a dry skillet over medium heat, toast the dried guajillo, ancho, and pasilla chiles for 1–2 minutes until fragrant, stirring frequently to prevent burning.
02 - Transfer toasted chiles to a bowl and cover with hot water. Let soak for 15 minutes until softened, then drain and reserve the soaking liquid.
03 - In the same skillet, roast the quartered onion, garlic cloves, and halved tomatoes until slightly charred, about 5 minutes.
04 - Combine softened chiles, roasted vegetables, apple cider vinegar, oregano, thyme, cumin seeds, peppercorns, cloves, and 1 cup beef broth in a blender. Process until completely smooth.
05 - Heat vegetable oil in a large Dutch oven over medium-high heat. Sear beef chunks and short ribs on all sides until deeply browned, working in batches if necessary.
06 - Pour blended sauce over the beef. Add remaining beef broth, bay leaves, cinnamon stick, and 2 tsp salt. Bring to a boil, then reduce heat to low. Cover and simmer for 2.5–3 hours until meat is fork-tender.
07 - Remove beef from the pot. Shred with two forks, discarding bones and excess fat. Skim excess fat from the birria consommé, reserving some for frying tortillas.
08 - Preheat oven to 375°F.
09 - 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.
10 - Fill each tortilla with shredded birria and a sprinkle of cheese. Roll up tightly and place seam-side down in a baking dish.
11 - Pour extra birria consommé over the enchiladas and top with remaining cheese.
12 - Bake for 10–15 minutes until cheese is melted and bubbly.
13 - Serve hot, garnished with diced white onion, chopped fresh cilantro, and lime wedges on the side.