Combine brown sugar, cocoa, shortening, butter, salt, and milk in a medium saucepan. Cook over medium heat, stirring frequently, until mixture comes to a boil. Cook 3 minutes, stirring constantly. Remove from heat; cool.
Add powdered sugar and vanilla; beat on medium speed of electric mixer about 1 minute or until smooth and creamy. Add a small amount of milk to obtain spreading consistency, if necessary. Spread immediately on cake.