Preheat oven to 350.  In a large bowl, beat butter until creamy. Add powdered sugar; cream until light and fluffy. Add lemon zest and vanilla extract; beat well. Add flour and cornstarch into butter mixture and beat until well mixed.

Roll cookie dough into 1-inch balls. Place onto ungreased cookie sheets and bake 15 minutes or until bottoms are light brown. Remove from oven, carefully remove from baking sheet, and cool on wire racks (when warm the cookies are delicate). When cool, spread Lemon Frosting on top of cookies.

Makes 6 dozen cookies

Lemon Frosting
1/3 cup butter, room temperature
1 teaspoon grated lemon zest
1/3 cup fresh lemon juice
4 cups powdered sugar

In a medium bowl, combine butter, lemon zest, lemon juice, and powdered sugar; stir until well mixed. Spread on top of cookies. If frosting is too thick, thin with a little bit of lemon juice.