Preheat a dry skillet over medium heat and toast the guajillo and ancho chiles for about 1 minute per side. Move them to a heatproof bowl.

Cover the toasted chiles with hot water and let them soak for 15 minutes, then drain well.

Blend the softened chiles with quartered onion, garlic, apple cider vinegar, cumin, and oregano until smooth. Add a splash of soaking water if needed.

Season beef chunks with kosher salt. In a large pot or Dutch oven, heat over medium-high and sear beef in batches for 6 to 8 minutes until deeply browned.

Add the browned beef back to the pot with the blended chile sauce, beef broth, and bay leaves. Bring to a boil, then lower heat and simmer covered for 2.5 to 3 hours until beef is tender.

Remove beef, shred it, and skim the fat from the top of the broth for the consomé.

Lightly dip each corn tortilla in the reserved fat, then fill with shredded beef and cheese, and cook on a skillet until crisp and golden on both sides.

Serve hot with consomé for dipping, diced onion, chopped cilantro, and lime wedges.