Toast guajillo, ancho, and árbol chiles in a dry skillet for 30–60 seconds per side until fragrant. Transfer to a bowl and cover with ½ cup hot beef broth. Let soak for 15–20 minutes until softened.
Blend softened chiles with soaking liquid, garlic, cumin, oregano, cloves, and salt until smooth. Strain through a fine-mesh sieve for a silky sauce. Set aside.
Season beef generously with salt and pepper. Heat oil in a Dutch oven over medium-high heat. Sear beef in batches until browned on all sides, 3–4 minutes per side. Remove and set aside.
Add chile sauce, beef broth, vinegar, onion, garlic, tomatoes, bay leaves, oregano, cumin, and cinnamon to the pot. Stir and return beef to the pot, ensuring it's mostly submerged.
Bring to a boil, then reduce to low. Cover and braise in a 350°F (175°C) oven for 2½–3 hours, or simmer on the stovetop for 3 hours, until beef is fork-tender.
Remove beef and shred with two forks. Strain braising liquid into a bowl to make the consomé. Skim fat if desired and keep warm.
Dip tortillas briefly into the warm consomé. Place on a skillet, add cheese and shredded beef to one half, then fold over.
Cook 2–3 minutes per side over medium heat until golden and crisp, pressing gently with a spatula. Repeat for all tortillas.
Serve tacos immediately with small bowls of hot consomé for dipping. Garnish with chopped cilantro, diced onion, and lime wedges.