01 - Heat a dry skillet over medium heat. Add dried guajillo, ancho, and pasilla chiles, toast 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 quartered onion, garlic cloves, and halved Roma tomatoes until slightly charred, about 5 minutes.
03 - Drain soaked chiles and transfer to a blender. Add roasted vegetables, apple cider vinegar, dried oregano, dried thyme, cumin seeds, peppercorns, cloves, and 1 cup beef broth. Blend until completely smooth.
04 - Heat vegetable oil in a large Dutch oven over medium-high heat. Season beef chuck and short ribs with salt. Sear meat on all sides until well-browned, about 3-4 minutes per batch.
05 - 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 and easily shreds.
06 - Remove beef from the pot. Using two forks, shred the meat, discarding bones and excess fat. Skim excess fat from the birria consommé, reserving 2-3 tbsp for frying tortillas.
07 - Preheat oven to 375°F.
08 - Dip each corn tortilla in the warm birria consommé for 2 seconds. Heat a skillet with a small amount of reserved fat over medium-high heat. Briefly fry each tortilla until pliable, about 10-15 seconds per side.
09 - Fill each tortilla with shredded birria and a sprinkle of cheese. Roll up tightly and place seam-side down in a baking dish.
10 - Pour extra birria consommé over the enchiladas and top with remaining cheese. Bake for 10-15 minutes until cheese is melted and bubbly.
11 - Serve hot, garnished with diced white onion, chopped fresh cilantro, and lime wedges on the side.