Remove stems and seeds from the dried chiles.
Toast the chiles lightly in a dry skillet.
Soak the toasted chiles in hot water for 15 minutes.
Blend soaked chiles, tomatoes, onion, garlic, vinegar, cumin, oregano, paprika, cinnamon, and a little broth until smooth.
Season the beef generously with salt and pepper.
Sear the beef on all sides until browned.
Transfer the beef to a large pot or Dutch oven.
Pour the blended chili sauce over the beef.
Add the remaining beef broth and bay leaves.
Bring to a gentle boil.
Cover and simmer for about 3–3½ hours until the beef is fork-tender.
Remove the beef and shred it.
Strain the broth to make a smooth consommé.
Dip each tortilla into the consommé.
Heat a lightly oiled skillet over medium heat.
Place the dipped tortilla on the skillet.
Add cheese and shredded birria to one half.
Fold the tortilla and cook until crispy on both sides.
Repeat with the remaining tortillas.
Garnish with cilantro and diced onion.
Serve hot with lime wedges and warm consommé for dipping.
