In a slow-cooker, combine the potatoes, carrots, celery, onion and green pepper. Top with the bratwurst slices. Combine the broth, salt, basil, and pepper; pour over top. Cover and cook on low for 7 hours or until vegetables are tender and sausage is no longer pink.
Stir in cream. Combine cornstarch and water until smooth; stir into stew. Cover and cook on HIGH for 30 minutes or until gravy has thickened.