Season the chuck roast on all sides with the salt and black pepper. Set it aside while you prepare the vegetables.
Place the carrots, potatoes, parsnips, and onion in the bottom of the slow cooker. Sprinkle the minced garlic, thyme, and rosemary over the vegetables.
Set the seasoned roast on top of the vegetables. Stir the Worcestershire sauce into the beef broth, then pour the mixture around the sides of the roast.
Cover the slow cooker and cook on low for 8 hours. The beef should be fork-tender and the vegetables soft when done.
Remove the roast and vegetables to a serving platter. If desired, skim fat from the remaining liquid and serve it as a simple gravy alongside the meal.