Combine flour, corn starch and powdered sugar in medium bowl; set aside.
Beat butter in large bowl with mixer at medium speed until smooth. Add flour mixture and vanilla; beat until well blended. (If necessary, refrigerate dough 30 minutes to 1 hour or until easy to handle.)
Preheat oven to 350°F. Shape dough into 1-inch balls. Place 2 inches apart on ungreased baking sheets; flatten slightly with floured fork.
Bake 10 to 12 minutes or until edges are lightly browned. Remove; cool completely on wire racks. Store in a tightly covered container.