Combine kraut and basil in saucepan. Cover and cook over low heat, stirring occasionally, 10 minutes; drain. Top bun halves with cheese slices and broil 5 to 7 inches from source of heat 3 to 5 minutes or until browned.
Cut 10 deep slits in each frankfurter without cutting all the way through. Broil 5 to 7 inches from source of heat 3 to 5 minutes. Turn and broil 3 minute longer. Place frankfurters on bun bottoms; top with kraut mixture and bun tops.