1 Mix the fats, sugar, and extracts: In the bowl of a stand mixer fitted with the paddle attachment, place the butter, shortening, sugar, baking powder, vanilla and peppermint extract and salt.
Mix on slow speed until most of the ingredients are blended, then increase to medium speed and mix until the butter is creamy and clings to the side of the bowl, about 2 minutes. Scrape down the sides of the bowl halfway through mixing and then afterwards.
2 Add the eggs and flour: Add the egg and egg white to the bowl and mix until incorporated. Scrape down again.
Add the flour and turn the mixer to low. Once most of the flour has been absorbed, increase the speed to medium low until no dry flour remains. Scrape down the sides of the bowl once or twice to make sure the dough is completely homogenized.
3 Prepare dough to chill: Scrape out the dough onto some plastic wrap. Pat the dough down into a 1-inch thick layer and then wrap tightly.
4 Chill dough: Refrigerate the dough for 2 hours or overnight. Once the dough has chilled, preheat the oven to 350°F. Line two baking sheets with parchment paper or silicon baking mats.
5 Roll the dough into balls: Break off chunks of the dough and roll them into 1 1/2-inch balls, roughly the size of a golf ball. Place them on the baking sheet, about 2 inches apart, then press them down into a disk with the palm of your hand or with the bottom of a flat glass. You want them to be about 1/2-inch thick disks that are about 2 1/4 inches in diameter (the size of a standard pint glass bottom).
6 Bake the cookies: Bake in the oven for 10 to 12 minutes or until the bottom of the cookie is starting to turn golden brown and the top of the cookie looks dry and baked. Try not to overbake them, as you want these cookies to be moist and tender in texture.
7 Cool: Let the cookies rest on the warm baking sheet for 5 minutes before moving them to a wire cooling rack to cool completely.
8 Make the frosting: Once the cookies have cooled completely, make the frosting by placing the butter in the clean bowl of a stand mixer fitted with the paddle attachment. Mix the butter on medium low speed until it starts to cling to the side of the bowl.
Add the powdered sugar, peppermint and vanilla extracts, and salt to the bowl and mix on slow speed until most of the sugar has been absorbed. Scrape down the sides of the bowl and increase the speed of the mixer to medium and beat until light and fluffy. Stop the mixer and add 2 tablespoons of the milk and the red food coloring. Be careful with the food coloring as it will stain.
Turn the mixer on slow and mix until the liquid is absorbed. Increase the speed to medium and beat the frosting until it is uniform in color. You may need to scrape down the sides of the bowl once or twice to make sure it’s completely homogenous in color. If the frosting seems too thick, add more milk, 1 teaspoon at a time, to thin it down.
9 Frost the cookies: Frost the top of each cooled cookie, then decorate the cookies with the white snowflake sprinkles.
10 Pair with Real Milk: Pour yourself a glass of real milk and enjoy!