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Step 1
Add the chiles to a large skillet over low heat. Toast the chiles for three to four minutes, tossing often, until the outside of the chiles are lightly toasted. With 30 seconds left, add the chile de árbol and toast until fragrant. Add one cup of beef stock, and bring the liquid to a simmer. Once simmering, remove from the heat, and cover with a lid. Allow to steep for 15-20 minutes.
Step 2
While the mixture is steeping, preheat a large Dutch oven over medium-high heat. Add vegetable oil. Then, season the beef with salt and, working in batches, sear on each side until golden brown. Remove the pot from the heat and set aside while you make the chili mixture.
Step 3
Optionally, char the onion over an open stove flame, or place it on a small sheet tray and broil for a few minutes, or until lightly charred. Set aside.
Step 4
Once the chiles have softened, use a spider to transfer to a high-powered blender, reserving the liquid. Add the cumin seeds, garlic, oregano, onion, and one and a half cups of reserved chili liquid. Blend until fully pureed, about one to two minutes.
Step 5
Pour the mixture over a fine mesh sieve set over the Dutch oven. Add the tomato puree, cinnamon stick, bay leaves, cloves, black peppercorns, and white vinegar to the pot, as well as the remaining beef stock, if more liquid is needed. The beef should not be covered, but it should come up at least ¾ of the way. Cover and braise for three and a half to four hours, or until the beef is falling apart and tender.
Step 6
Remove the beef from the pot and strain the cooking liquid. Add half of the strained liquid into a serving bowl and add chopped cilantro and onion, this will be the consomé. Then, shred the beef, and add it back to the other half of the reserved liquid, without the onion and cilantro.
Step 7
Preheat a medium skillet over medium heat.
Step 8
Dip one tortilla at a time into the consomé.
Step 9
Add Oaxacan cheese to the corn tortilla. Top with a portion of the shredded beef, followed by a bit more cheese. Fold the tortilla in half.
Step 10
Add the quesabirria to the preheated skillet and cook for three minutes, or until golden brown. Drizzle a spoonful of the consomé onto the uncooked side before turning over. Then flip and repeat on the other side.
Step 11
Transfer to a plate, and let it cool slightly. Repeat as needed.
Step 12
Serve the quesabirria with consomé, lime, cilantro, and onion.