Preheat oven to 350°F. In medium bowl combine cornstarch, flour and 2/3 cup of powdered sugar, set aside. In a large bowl, beat 2 cups of butter with a mixer at medium speed until softened and smooth. Add the cornstarch mixture, vanilla, and 1 1/2 tsp. lemon peel; beat well. (If necessary, refrigerate dough 1 hour or until easy to handle).
Shape the dough into 1-inch balls and place them 1 1/2 inches apart on ungreased cookie sheets.
Bake 10 - 12 minutes, or until edges are lightly browned. Cool completely on wire racks.
For icing, beat together in medium bowl the remaining 1/3 cup of butter and the remaining tsp. of lemon peel until the butter is softened. Add the remaining 4 cups of powdered sugar and lemon juice; beat until well combined. Add red food coloring.