Place the beef stew meat and flour in a bowl and toss until the meat is lightly coated.
Heat a skillet over medium heat and brown the coated beef on all sides for a few minutes. Transfer the beef to the slow cooker.
Add the carrots, potatoes, parsnips, and onion to the slow cooker.
In a small bowl, whisk together the beef broth and tomato paste until smooth, then pour the mixture over the meat and vegetables.
Add the dried thyme, bay leaves, salt, and black pepper. Stir gently to combine.
Cover and cook on low for 8 hours or until the beef is fork-tender.
Remove the bay leaves before serving and sprinkle with chopped parsley.