Toast the dried guajillo, ancho, and pasilla chilies in a dry skillet over medium heat for 1-2 minutes until fragrant, being careful not to burn them.
Place the toasted chilies in a bowl and cover with hot water. Let soak for 15 minutes until softened.
Drain the chilies and transfer them to a blender. Add beef broth, quartered onion, garlic cloves, quartered tomatoes, apple cider vinegar, ground cumin, dried oregano, ground cinnamon, smoked paprika, ground cloves, ground black pepper, and salt.
Blend the mixture until smooth, adding a little water if needed to reach a sauce consistency.
Heat vegetable oil in a large skillet over medium-high heat. Sear the beef chuck roast chunks on all sides until browned, about 3-4 minutes per side. Work in batches if necessary to avoid overcrowding.
Transfer the seared beef to the slow cooker. Pour the blended chili sauce over the beef and add the bay leaves.
Cover and cook on low for 8 hours, or until the beef is very tender and easily shredded with a fork.
Remove the beef from the slow cooker and shred it using two forks. Discard the bay leaves.
Return the shredded beef to the slow cooker and stir to coat with the sauce.
Serve the beef birria hot, garnished with chopped fresh cilantro, diced white onion, and lime wedges. Warm corn tortillas on the side for tacos or use the birria as desired.