Preheat the oven to 325°F and line two baking sheets with parchment paper and set aside.
To make the dough, begin by mixing together the cake flour, baking powder, baking soda, and salt in a medium sized bowl.
In the bowl of an electric mixer fitted with a paddle attachment, combine the sugar, butter, vegetable shortening, and sour cream and mix on medium-high speed for about 3 minutes until it is smooth, light and fluffy.
Next, add the egg, vanilla, and peppermint extract and mix until everything is combined.
Slowly add the flour mixture to the egg and sugar mixture and mix on low until everything is combined, about 1 minute.
Form the dough into balls using a medium cookie scoop then roll them with your hands to make smooth balls. Place dough balls on the prepared cookie sheets, leaving 2 inches between them.
Press the dough balls down with the bottom of a cup.
Bake the cookies for 10 to 13 minutes until the tops are set and pale yellow. Make sure you don’t overcook; these cookies are amazing under cooked!
Cool the cookies on the pan then transfer to a wire rack until they have completely cooled.
Make the frosting by beating the butter and peppermint extract in a stand mixer fitted with the paddle until combined.
Add the powdered sugar one cup at a time. Then thin it out with milk or heavy cream to desired consistency.
Frost the tops of the cookies and sprinkle with crushed peppermint chips and sprinkles.