In a dry skillet over medium heat, toast the dried chilies for about 30 seconds on each side until they become fragrant. Then, transfer them to a bowl and cover with hot water. Let them soak for 15-20 minutes until softened.
In a blender, combine the soaked chilies, chopped onion, minced garlic, dried oregano, ground cumin, smoked paprika, ground cinnamon, beef broth, and apple cider vinegar. Blend until smooth to form the birria marinade.
Season the beef chunks with salt and pepper, then place them in a large bowl or resealable plastic bag. Pour the birria marinade over the beef, ensure the beef is well coated. Marinate in the refrigerator for at least 4 hours, or preferably overnight.
Preheat the oven to 325°F (163°C).
Transfer the marinated beef and marinade to a large Dutch oven or roasting pan. Cover with a lid or foil and bake for 3-4 hours, or until the beef is very tender and easily shreds with a fork.
Once the beef is cooked, remove it from the pan and shred it using two forks. Skim off any excess fat from the cooking liquid.
Serve the beef birria in bowls, ladled with some of the cooking liquid. Accompany with warm corn tortillas, fresh cilantro, diced onion, and lime wedges on the side for guests to garnish their own servings as desired. Enjoy!