In a dry skillet over medium heat, add the guajillo and ancho chiles. Toast them for approximately 1-2 minutes, or until they become fragrant. Once toasted, transfer the chiles to a bowl and cover with hot water. Allow them to soak for 15 minutes until softened, then drain well.
In a blender or food processor, combine the soaked chiles, minced garlic, cumin, oregano, smoked paprika, and apple cider vinegar. Blend the mixture until it reaches a smooth and homogenous paste, adding a splash of beef broth if necessary to facilitate blending.
Generously season the beef chuck roast with salt and pepper. In a skillet heated to medium-high, sear the beef on all sides until a deep brown crust forms (about 3-4 minutes per side).
Begin by layering the chopped onion at the bottom of the crockpot. Next, place the seared beef chuck roast on top of the onions. Spoon the blended sauce evenly over the beef, then pour in the remaining beef broth.
Securely cover the crockpot and set it to cook on low for 8 hours or on high for 4 hours, or until the beef is fork-tender and can be easily shredded.
Once cooked, carefully remove the beef from the crockpot and place it on a cutting board. Use two forks to shred the beef into bite-sized pieces. Return the shredded beef to the crockpot, stirring it well to mix with the sauce.
Warm the corn tortillas either in a skillet over low heat or directly over an open flame until they are pliable and heated through. Fill each tortilla generously with the tender shredded birria, and top with freshly chopped cilantro.
Present the tacos with lime wedges on the side for squeezing over, along with a small bowl of the reserved cooking liquid for dipping.
Notes
Pair with pickled onions or fresh salsa for added flavor.