01 - In a dry skillet over medium heat, toast the dried chiles for 1–2 minutes until fragrant.
02 - Place the chiles in a bowl and cover with hot water; soak for 15 minutes until softened.
03 - In the same skillet, roast onion, garlic, and tomatoes until slightly charred, about 5 minutes.
04 - Transfer softened chiles, roasted vegetables, vinegar, oregano, thyme, cumin, peppercorns, cloves, and 1 cup beef broth to a blender; blend until smooth.
05 - In a large Dutch oven, heat vegetable oil over medium-high heat. Sear beef chunks and short ribs on all sides until browned.
06 - Pour blended sauce over beef; add remaining 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 very tender.
07 - Remove beef from the pot. Shred with two forks, discarding bones and excess fat. Skim excess fat from the birria consommé (reserve some for frying tortillas).
08 - Preheat oven to 375°F (190°C).
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 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 onion, chopped cilantro, and lime wedges.