Make the Cookie Dough : In a large bowl, use a handheld or stand mixer to cream the softened butter and confectioners’ sugar together until light and fluffy, about 2–3 minutes. Add the egg yolk, vanilla extract, and peppermint extract. Beat until well combined. In a separate bowl, whisk together the flour, cornstarch, baking powder, and salt. Gradually add the dry ingredients to the wet ingredients, mixing just until combined. Be careful not to overmix. Cover the dough and refrigerate for at least 30 minutes. This helps the dough hold its shape while baking.

Bake the Cookies : Preheat your oven to 350°F (175°C) and line two baking sheets with parchment paper. Scoop tablespoon-sized portions of dough and roll them into balls. Place them on the prepared baking sheets about 2 inches apart. Bake for 10–12 minutes, or until the edges are set but the cookies remain pale. Avoid overbaking to maintain the meltaway texture. Let the cookies cool on the baking sheet for 5 minutes, then transfer to a wire rack to cool completely.

Prepare the Buttercream : In a medium bowl, beat the softened butter until creamy. Add the confectioners’ sugar, milk, vanilla extract, and peppermint extract. Beat until smooth and fluffy. If desired, add a drop of red or pink food coloring and mix until evenly incorporated.

Frost and Decorate : Once the cookies are completely cool, spread a small amount of buttercream on the top of each cookie using a knife or piping bag. Sprinkle crushed candy canes over the frosting for a festive finish.

Serve and Enjoy : Allow the frosting to set for about 15 minutes before serving or storing. Store cookies in an airtight container at room temperature for up to 3 days or in the refrigerator for up to a week.