In a large pot or Dutch oven, add the beef chuck roast and cover it with beef broth. Bring to a boil and then reduce to a simmer.

Remove the stems and seeds from the guajillo and ancho chiles. Toast them lightly in a dry skillet for about 2-3 minutes until fragrant.

Place the toasted chiles in a blender with chopped onion, minced garlic, apple cider vinegar, cumin, oregano, paprika, salt, and pepper. Add a cup of the cooking broth and blend until smooth.

After the meat has simmered for about an hour, add the blended sauce to the pot with the meat. Continue simmering for another hour, until the meat is tender and shreds easily.

Remove the beef from the pot and shred it using two forks. Set aside and reserve the consomme for serving.

Warm the corn tortillas in a skillet until soft and pliable. Fill each tortilla with shredded beef and a sprinkle of cheese. Roll them up tightly.

Place the enchiladas seam side down in a baking dish or skillet. Pour a ladle of the reserved consomme over the top and sprinkle more cheese if desired.

Cover with aluminum foil and bake in a preheated oven at 350°F (175°C) for 20-25 minutes, until heated through and the cheese is melted.

Serve the enchiladas hot, garnished with chopped cilantro, lime wedges, and additional diced onions, and enjoy the remaining consomme as a dipping sauce.