Prep the chiles. Remove stems and seeds. Toast chiles in a dry skillet over medium heat for 30–45 seconds per side until fragrant.
Don’t burn them.
Soften the chiles. Cover with hot water and soak 15 minutes until pliable. Reserve 1 cup of the soaking liquid.
Build the sauce. In the same skillet, sear onion quarters and garlic until lightly charred. Blend soaked chiles, onion, garlic, tomatoes, cumin, oregano, paprika, coriander, vinegar, and 1 cup stock (plus a splash of chile soaking liquid) until smooth.
Season and sear the beef. Cut beef into large chunks.
Pat dry, season well with salt and pepper. Sear in a heavy pot with a little oil until browned on all sides.
Simmer. Pour the blended sauce over the beef. Add remaining stock, bay leaves, and cinnamon stick.
The liquid should mostly cover the meat; add water if needed. Bring to a gentle boil, then reduce to low, cover, and simmer 2.5–3 hours, until fork-tender.
Shred the meat. Remove beef and shred with two forks. Skim excess fat from the top of the consomé, reserving a few tablespoons for frying the tortillas.
Adjust seasoning. Taste the consomé and adjust salt, pepper, and a splash more vinegar if it needs brightness.
Assemble tacos. Heat a skillet over medium.
Lightly brush tortillas with the reserved birria fat or consomé. Lay tortillas down, sprinkle cheese on half, add shredded beef, and fold.
Crisp and melt. Cook 2–3 minutes per side until the tortilla is crisp and the cheese melts. Work in batches.
Serve. Ladle hot consomé into small bowls.
Top tacos with cilantro and diced onion. Serve with lime wedges for squeezing. Dip tacos into the consomé and enjoy.