Place dried guajillo, ancho, and pasilla chilies in a medium bowl and cover with hot water. Let soak for 20 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, ground cinnamon, ground black pepper, and salt. Blend until smooth to create the birria sauce.
Heat vegetable oil in a large skillet over medium-high heat. Sear beef chuck roast chunks on all sides until browned, about 3-4 minutes per side. Work in batches if necessary. Transfer seared beef to the slow cooker.
Pour the blended birria sauce over the beef in the slow cooker. Add bay leaves and stir gently to combine.
Cover and cook on low for 8 hours, or until the beef is very tender and shreds easily with a fork.
Remove bay leaves and shred the beef directly in the slow cooker using two forks. Stir to combine the shredded beef with the sauce.
To serve, warm corn tortillas and fill with the shredded beef birria. Garnish with chopped white onion and fresh cilantro. Serve with lime wedges and a side of the birria consommé for dipping.