Preheat oven to 350 degrees F (175 degrees C). Whisk together the cake flour, cornstarch, and confectioners' sugar; set aside.
Beat the butter, vegetable oil, superfine sugar, and vanilla extract with an electric mixer in a large bowl until smooth. Mix in the flour mixture until just incorporated. Roll dough into 1 inch balls. Place 2 inches apart on ungreased baking sheets, and flatten each cookie slightly with the bottom of a glass.
Bake in the preheated oven until golden, about 12 minutes. Allow the cookies to cool on the baking sheet for 1 minute before removing to a wire rack to cool completely.