In slow cooker bowl, stir together ground turkey, carrots, onion, celery, garlic, tomato paste, vinegar, brown sugar, Worcestershire sauce, paprika and dry mustard. Cover and cook on HIGH for 3 hours or LOW for 6 hours, stirring turkey mixture halfway through cooking time.
Stir in salt. Spoon 1/3 cup of the turkey mixture on each bun and serve immediately.