Toast dried chiles in a dry skillet over medium heat for 30-60 seconds per side until fragrant, then soak in boiling water for 15-20 minutes.
Blend soaked chiles with canned tomatoes, onion, garlic, cumin, oregano, smoked paprika, cinnamon, cloves, vinegar, and 1 cup beef broth until smooth. Strain through a fine-mesh strainer.
Pat beef dry, season with salt, and sear in hot oil in a Dutch oven for 3-4 minutes per side until deeply browned. Work in batches.
Pour strained chile sauce into the pot, scraping up browned bits. Add remaining beef broth, return beef with bay leaves, bring to a boil, then simmer covered for 2.5-3 hours until fork-tender.
Remove beef and shred with two forks. Skim fat from the broth and reserve in a shallow dish. Keep the consomé warm for dipping.
Heat a skillet over medium-high heat. Dip each tortilla in reserved consomé fat, coating both sides. Place on the skillet and add cheese, shredded beef, onion, and cilantro.
Cook for 2-3 minutes until cheese melts and bottom is golden and crispy. Fold in half and cook 1-2 minutes more until second side is golden. Repeat with remaining tortillas.
Serve immediately with warm consomé for dipping, lime wedges, extra onion, and cilantro.