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 heatproof bowl and cover with hot water. Let soak for 15 minutes until completely softened.
03 - In the same skillet, roast 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 chuck chunks and short ribs on all sides until well-browned, working in batches if necessary.
06 - Pour blended sauce over browned beef. Add 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 meat is fork-tender.
07 - Remove beef from pot, reserving the cooking liquid. Shred meat with two forks, discarding bones and excess fat. Skim excess fat from the consommé, reserving some for frying tortillas.
08 - Preheat oven to 375°F.
09 - Briefly dip each corn tortilla in warm birria consommé, then fry in a hot skillet with a small amount of reserved fat for 10-15 seconds per side until pliable.
10 - Fill each tortilla with shredded birria and a portion of cheese. Roll up tightly and place seam-side down in a baking dish.
11 - Pour additional birria consommé over the assembled enchiladas. Sprinkle remaining cheese evenly across the top.
12 - Bake for 10-15 minutes until cheese is fully melted and bubbly.
13 - Serve hot, generously garnished with diced white onion, chopped fresh cilantro, and lime wedges on the side.