Preheat oven to 350 degrees.
Cream together butter, powdered sugar, vanilla, and salt. Gradually add cornstarch and flour. Whip with an electric mixer until fluffy.
Place into a cookie press and press cookies out onto cool, ungreased baking sheets. Decorate with candied cherries or colored sugar if desired. Bake 12 to 15 minutes. Let cool for 2 minutes on baking sheet, then remove to wire rack to cool completely.