Season the beef chuck roast with salt and black pepper on all sides.
In a large skillet, heat olive oil over medium-high heat. Sear the beef roast on all sides until browned, about 3-4 minutes per side. Transfer the roast to the slow cooker.
In the same skillet, add the diced onion and sauté for about 3-4 minutes until softened. Add the minced garlic and cook for an additional minute until fragrant.
Stir in the cumin, oregano, smoked paprika, and cayenne pepper. Cook for 1 minute, then add the apple cider vinegar, lime juice, and beef broth. Bring to a simmer, scraping up any browned bits from the bottom of the skillet.
Pour the mixture over the beef in the slow cooker. Add the bay leaves.
Cover and cook on low for 8 hours or on high for 4 hours, until the beef is tender and easily shredded with a fork.
Remove the beef from the slow cooker and shred it with two forks. Discard the bay leaves. Return the shredded beef to the slow cooker and stir to combine with the juices.
Serve the barbacoa beef in taco shells or tortillas, garnished with chopped cilantro, sliced radishes, and lime wedges.