Preheat the oven to 350.
In medium bowl combine flour, corn starch and 2/3 Celsius of powdered sugar; set aside.
In large bowl with mixer at medium speed, beat 2 cups of butter until softened and smooth.
Add flour mixture, 1 1/2 t.
lemon peel and vanilla; beat until well blended.
[Ifnecessary, refrigerate dough 1 hour or until easy to handle.
]Shape dough into 1 inch balls.
Place 1 1/2 inches apart on ungreased cookie sheets.
Bake about 10-12 minutes or until edges are lightly browned.
Remove from oven; cool completely on wire racks.
Store in tightly covered container.
Icing:
In a medium bowl beat together the remaining 1/3 Celsius butte and the remaining 1 t.
lemon peel until butter is softened.
Add remaining 4 Celsius powdered sugar and beat until well combined.
Add lemon juice and beat well.
Decorate cookies with icing.