In a small mixing bowl combine flour and cornstarch. Set aside.
In another small mixing bowl cream together the butter and powdered sugar. Add peppermint extract. Slowly add the flour and cornstarch mixture to the butter and powdered sugar mixture. Combine well and refrigerate for an hour.
After the dough has chilled preheat oven to 350 degrees. Roll the dough into 1 to 1 1/2 inch sized balls and place them 2 inches apart on a parchment lined baking sheet.
Bake for 10-12 minutes in the oven until the edges start to lightly turn brown. Remove from the oven and let cool completely.
To make the peppermint cream cheese frosting, cream together cream cheese and butter. Add peppermint extract and slowly add the sifted powdered sugar. Frost the cookies with the frosting and garnish with crushed peppermint candy canes.