Preheat the oven to 350 degrees F. Line a baking sheet with parchment paper and set aside. Mix together dry ingredients in a large mixing bowl - all purpose flour, cornstarch, kosher salt, and baking powder.
In the bowl of a stand mixer fitted with the paddle attachment, cream together butter and sugar for 2-3 minutes, until light and fluffy. Scrape down the sides of the bowl and add the egg, vanilla extract, and peppermint extract. Mix for 1 minute on medium speed, then add the dry ingredients to the wet ingredients.
Mix for 1 minute on medium speed, then add the dry ingredients to the wet ingredients. Mix on low, then gradually increase speed until the dough has a smooth texture. It should be the consistency of clay.
On a lightly floured work surface, use a rolling pin to roll out the dough until it's about a 1/2 inch thick. Use a 3 inch round cookie cutter to cutout the cookies.
Place cookies onto a baking sheet, about 2 inches apart. Bake for 8-10 minutes, until the centers of the cookies are slightly puffy. Be careful not to overbake as this will make the cookies dry.
Allow the cookies to cool on the baking sheet for 5 minutes, then transfer to a wire rack to cool completely.
While the cookies are baking, prepare the cream cheese frosting. Add butter to the bowl of a stand mixer fitted with the paddle attachment. Beat on medium speed for 1 minute, then begin adding powdered in one cup increments.
Once all of the sugar is added, scrape down the sides of the bowl and continue to mix on medium speed. Add in the peppermint extract, kosher salt, and cold cream cheese. Continue to mix until the cream cheese is just combined, about 30 seconds.
Add about 2/3 of the cream cheese frosting to a separate bowl and mix in the red food coloring with a spoon until it appears to be uniform red color.
Fit 2 piping bags with your favorite piping tips (I used the 1M piping tip). Add the red frosting to one and the white frosting to another.
Add candy canes to a ziploc bag. Use a rolling pin to smash the candy canes into pieces.
Once the cookies have cooled completely, use the red piping bag to draw a line down the middle on the cookie. Then draw a line to make a cross on the cookie. Draw one more line to make a 6-point star on the cookie.
Sprinkle crushed candy cane pieces on top, then use the white frosting to fill in the empty space on the cookie to make them look like real peppermint candies!
Notes
Use a kitchen scale to measure out your ingredients. It's far more accurate than a measuring cup and allows for the best results every time!
Be careful not to overbake the cookies. Once the centers are a little puffy and the edges appear set, remove them from the oven. You do not want them to be golden brown, if so, they are overbaked.