In a bowl, cream the butter and sugar together until smooth. Add in flour and cornstarch and stir well combined.
Cover or wrap in plastic wrap and chill for at least 30 minutes.
Roll dough into 1 inch balls and place on cookie sheets lined with parchment. Bake at 325 degrees for about 15-18 minutes.
Cool completely on cooling racks.
For frosting: In a bowl beat vanilla, shortening, butter, powdered sugar, and milk together until smooth and creamy. Mix in food coloring if desired. Pipe frosting on top of cooled cookies. Makes 3 dozen cookies.