Ingredients

2 1/2 cups cake flour , plus more for dusting work surface
2 tsp cornstarch
1 1/2 tsp baking powder
1/2 tsp salt
1/2 cup unsalted butter , at room temperature
1/4 cup all vegetable shortening (unflavored), at room temperature
1 cup granulated sugar
1 large egg
1 large egg white
2 tsp vanilla extract
1/2 tsp peppermint extract
Crushed candy canes , for topping
Peppermint Cream Cheese Frosting
4 oz cream cheese , softened
4 Tbsp unsalted butter
1/2 tsp peppermint extract
2 1/2 cups powdered sugar

Instructions

Sift flour, cornstarch, baking powder and salt into a large bowl, then whisk it just a few times, set aside. In the bowl of an electric stand mixer, on medium speed, whip together butter, shortening and sugar until very pale and fluffy, about 4 minutes, scrapping down the sides of the bowl as needed. Add in egg and mix until combine, then add egg white, vanilla and peppermint extract and mix until combine. With mixer running, slowly add in dry ingredients and mix just until combine. Transfer dough to an airtight container and refrigerate 2 hours. Preheat oven to 375 during the last 10 minutes of refrigeration.
Scoop dough out about 3 Tbsp at a time and roll
into a ball. Place dough ball on a lightly floured surface, sprinkle top lightly with flour, then using something flat and smooth (such as the storage container lid), press and evenly flatten dough to 1/2" thick. Transfer flattened dough to a Silpat or parchment paper lined baking sheet and repeat process with remaining dough (you'll have to use 2 cookie sheets). Bake in preheated oven 9 - 11 minutes. Allow to cool 5 minutes on baking sheet before transferring to a wire rack to cool. Cool completely then frost with Cream Cheese Frosting and sprinkle with crushed candy canes.
For the frosting:
In the bowl of an electric stand mixer fitted with the paddle attachment, whip together cream cheese and butter until pale and fluffy. Add peppermint extract and powdered sugar and mix until pale and fluffy.