Toast the dried guajillo, ancho, and pasilla chilies in a dry skillet over medium heat for 1-2 minutes until fragrant, turning frequently to avoid burning.
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, diced tomatoes, apple cider vinegar, ground cumin, dried oregano, smoked paprika, black pepper, and salt to the blender.
Blend the mixture until smooth to create the birria sauce.
Heat vegetable oil in a large skillet over medium-high heat.
Sear the beef chuck roast chunks in the hot oil until browned on all sides, about 3-4 minutes per side. Work in batches if needed.
Transfer the seared beef to the slow cooker.
Pour the blended birria sauce over the beef in the slow cooker.
Add the bay leaves to the slow cooker and stir gently to combine.
Cover and cook on low for 8 hours, or until the beef is tender and easily shredded with a fork.
Remove the bay leaves from the slow cooker.
Shred the beef directly in the slow cooker using two forks and stir to coat with the sauce.
Serve the beef birria hot with warm corn tortillas, garnished with chopped white onion, fresh cilantro, and lime wedges.