Toast the dried chiles in a dry skillet over medium heat for 1-2 minutes per side until fragrant but not blackened, then transfer to a bowl and cover with boiling water for 15 minutes to soften.⏱ 2 min
While chiles soak, toast the cumin seeds, peppercorns, cloves, and cinnamon stick in the same dry skillet over medium heat for 2 minutes until very fragrant, shaking the pan often.⏱ 2 min
Char the quartered onion, garlic cloves, and tomato halves in the skillet cut-side down for 5-7 minutes until blackened in spots.⏱ 7 min
Drain the soaked chiles and add them to a blender with the charred vegetables, toasted spices, oregano, vinegar, and 1 cup of the beef stock, then blend until completely smooth, about 2 minutes.⏱ 2 min
Season the beef chunks generously with the salt, then sear them in a large heavy pot or Dutch oven over medium-high heat in batches until browned on all sides, about 8 minutes total.⏱ 8 min
Return all the beef to the pot, pour the blended chile sauce over it, add the remaining 3 cups stock and the bay leaves, then bring to a boil.
Cover the pot tightly with a lid or foil, reduce heat to low, and braise for 2.5 to 3 hours until the beef shreds easily with a fork.⏱ 180 min
Remove the beef from the pot and shred it with two forks, discarding any large fat pieces, then return the shredded meat to the pot and stir to coat with the consommé.
Skim about 1/2 cup of the red fat from the top of the consommé and set it aside in a small bowl for dipping the tortillas.
Heat a griddle or large skillet over medium-high heat, dip a tortilla in the reserved red fat to coat both sides, then lay it flat on the griddle.
Add a handful of cheese to one half of the tortilla, top with a generous spoonful of shredded birria, fold the tortilla in half, and press gently with a spatula.
Cook for 2-3 minutes per side until the tortilla is crispy and golden-red and the cheese is melted, then transfer to a plate.⏱ 3 min
Repeat with remaining tortillas and filling, working in batches and adding more reserved fat to the griddle as needed.
Serve the tacos hot with a bowl of the warm consommé on the side for dipping, plus diced onion, cilantro, and lime wedges.
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Chef’s tip · Birria tastes even better the next day — refrigerate the meat and consommé separately overnight so you can lift off the solidified fat easily, then reheat and assemble fresh tacos.
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