Place ingredients in the slow cooker in the following order: carrots, celery, potatoes, onions, garlic, bay leaf, Worcestershire, thyme, basil, pepper, beef, tomatoes with juice, and broth. Cover and cook on low 8 to 9 hours.
Remove beef and vegetables to large serving bowl; cover and keep warm. Remove and discard bay leaf. Turn slow cooker to high, cover. In a small bowl, stir water into flour until smooth. Add 1/2 cup cooking liquid; mix well. Stir flour mixture into slow cooker. Cover and cook 15 minutes or until thickened. Pour sauce over meat and vegetables. Serve immediately.