Remove stems and seeds from the dried chiles, then place them in a bowl and pour hot (not boiling) water over them. Let soak about 15 minutes until soft.

Drain the chiles, then transfer to a blender. Add the quartered onion, garlic cloves, cumin, oregano, and about 1 cup of the beef broth. Blend until very smooth, adding more broth by tablespoonfuls if needed to get a silky puree.

Pat the chuck roast dry and season all over with salt and pepper.

Heat a large, oven-safe pot or Dutch oven over medium-high heat with a tablespoon of oil. Sear the roast 2–3 minutes per side until browned.

Pour the chile puree over the seared beef and add the remaining beef broth. Bring to a gentle simmer on the stovetop.

Cover the pot and transfer to a 325°F oven. Braise for about 3 hours, or until the beef pulls apart easily with forks.

Remove the roast and shred it with two forks. Skim any excess fat from the braising liquid and keep that liquid — it’s your consomé. Adjust salt and pepper.

Heat a skillet over medium. Dip a corn tortilla briefly into the warm consomé, lay it on the skillet, add a sprinkle of cheese and a generous spoonful of shredded beef, then top with another lightly dipped tortilla or fold and press down.

Cook until the cheese melts and the tortilla is crisp and golden, flipping once.

Serve hot with chopped cilantro, lime wedges, and a small bowl of the consomé for dipping.