Mix together butter and powdered sugar til smooth. Add flour, corn starch and vanilla and mix again until dough comes together. Cover and chill for 30 minutes.
Preheat oven to 350 degrees. Scoop about 2 tablespoons of dough and roll into a ball. Place on a lightly greased baking sheet. Repeat with remaining dough.
Gently press each dough ball with the heel of your hand to flatten slightly. Bake for 10-12 minutes, allow to cool completely on a cooling rack.
Make the frosting by creaming together cream cheese, and butter. Mix in powdered sugar and peppermint extract. If desired, mix in a drop or two or red food coloring. Spread over cooled cookies and top with crushed candy canes.
Notes
Recipe makes a lot of frosting, so if you aren't a frosting lover I would recommend halving the frosting or doubling the cookie portion of the recipe.