Season the chuck roast on all sides with the salt and black pepper. Place it in the bottom of the slow cooker.
Arrange the carrot chunks, potato quarters, parsnip chunks, and onion slices around the roast. Sprinkle the minced garlic over the top.
Stir the Worcestershire sauce into the beef broth. Pour the mixture over the meat and vegetables.
Lay the thyme sprigs, rosemary sprig, and bay leaf on top of the ingredients.
Cover and cook on low for 8 hours until the beef pulls apart easily with a fork.
Remove the roast and vegetables to a serving platter. Discard the herb sprigs and bay leaf.
Ladle 1 cup of the cooking liquid into a small bowl and whisk in the flour until smooth. Stir the mixture back into the slow cooker and cook on high for 10 minutes to thicken into gravy.
Slice or shred the beef and serve it with the vegetables and gravy.