Cream butter, slowly add cornstarch and 1/3 cup confectioners' sugar; beat til fluffy. Stir in flour with wooden spoon (very soft dough). Cover and chill 1 hour.
Preheat oven to 350 degrees F (180 degrees C).
Roll dough into 24, 1 inch balls. Place 1 and 1/2 inches apart on ungreased sheet. Press slight indentation on top of each cookie. Bake for 10-12 minutes until firm, not brown. Cool, top with icing.
To Make Icing: Blend cream cheese and 1 cup powdered sugar til smooth. Mix in vanilla or 1/4 t. of another extract and a few drops of food coloring. Mix well.
