Cream shortening and butter with electric mixer. Add cocoa or melted chocolate and vanilla. Gradually add sugar, one cup at a time, beating well on medium speed. Scrape sides and bottom of bowl often. When all sugar has been mixed in, icing will appear dry. Add milk and beat at medium speed until light and fluffy.
Add 3-4 tablespoons light corn syrup per recipe to thin icing if desired. Keep icing covered with a damp cloth until ready to use.