Season the 3 pounds beef chuck roast generously with 2 teaspoons salt and 1 teaspoon black pepper. Heat a heavy skillet to high heat. Sear the roast on all sides. Transfer roast to a 6-quart slow cooker.
Pour 1/4 cup Worcestershire sauce over the roast. Sprinkle 2 teaspoons minced garlic over the roast. Top with slices of 1 medium yellow onion.
Cover and cook on low for 8 hours until beef shreds easily with a fork.
In a small bowl stir together 1 cup sour cream, 2 tablespoons prepared horseradish, and 1/4 teaspoon salt.
Shred the beef in its juices with the onion. Serve divided on 12 hamburger buns (toasted or untoasted) and top with a spoonful of the creamy horseradish.