In a large pot or Dutch oven, place the beef chuck roast and cover it with water. Bring it to a boil, then reduce the heat to simmer for about 1 hour until the meat is tender.
While the meat cooks, remove the stems and seeds from the dried chilies. In a skillet, toast the chilies over medium heat for a few minutes until fragrant. Add the garlic and onion, cooking until softened.
Transfer the toasted chilies, garlic, onion, beef broth, apple cider vinegar, cumin, oregano, salt, and black pepper into a blender. Blend until smooth.
Once the meat is cooked, shred it using tongs or a fork and mix with the blended sauce until well combined.
Preheat your oven to 350°F (175°C).
To assemble the enchiladas, warm the corn tortillas in a separate skillet until pliable. Place 2-3 tablespoons of the birria mixture in the center of each tortilla, sprinkle with cheese, then roll tightly and place in a greased baking dish, seam side down.
Once all enchiladas are assembled, pour the reserved birria consomé over the top and sprinkle with additional cheese and chopped onions.
Cover the baking dish with aluminum foil and bake for 20 minutes. Remove the foil and bake for an additional 10 minutes, until cheese is bubbly and golden.
Garnish with fresh cilantro before serving.