Brush the chuck roast with 2 tablespoons of the butter on all sides. Season the beef with the sea salt and black pepper, rubbing it in evenly on all sides. Place the chuck roast on a plate and allow it to rest for 30 minutes, until the meat is at room temperature.
In a slow cooker, place the roast. Add the onion, radishes, and mushrooms around the roast. Drizzle the remaining 2 tablespoons of melted butter over the vegetables.
Pour the beef broth around the roast, to avoid removing the seasoning.
Submerge the rosemary, thyme, and bay leaves in the broth.
Cover and cook on LOW for 10 to 12 hours, flipping the meat halfway through cooking, until the beef is very tender. Slice and serve hot.