Remove stems and seeds from the dried guajillo and ancho chiles. Heat a skillet over medium heat and lightly toast the chiles for about 1 to 2 minutes until fragrant.
Place the toasted chiles in a bowl and cover with hot water. Let them soak for 10 to 15 minutes to soften.
In a blender, combine the soaked chiles, chopped onion, garlic cloves, apple cider vinegar, cumin, oregano, paprika, salt, and black pepper. Add 1 cup of the beef broth and blend until smooth.
Cut the beef chuck roast into large chunks and place them in the crock pot.
Pour the blended chile sauce over the beef. Add the remaining 3 cups of beef broth, cinnamon stick, and bay leaves to the crock pot.
Cover and cook on low heat for 8 hours or until the beef is fall-apart tender.
Once cooked, remove the beef and shred it using two forks. Skim any fat off the top of the consomé and reserve the broth for dipping or serving.
Heat a skillet over medium heat. Lightly dip each tortilla into the top of the consomé to coat one side with the broth, then place it on the hot skillet.
Sprinkle cheese on one half of the tortilla, add some shredded beef, and fold it over into a taco. Cook until crispy and golden, about 2 to 3 minutes per side.
Repeat with remaining tortillas. Serve hot with a bowl of the consomé for dipping, topped with diced onion, cilantro, and a squeeze of lime.