Preheat oven to 350 degrees F. Liberally grease a 24-cavity miniature muffin pan with cooking spray and set aside. Meanwhile, in the bowl of a stand mixer, beat together the butter, brown sugar and white sugar until creamy. Stir in egg and vanilla. Lastly, beat in the dry cake mix, flour, baking soda and salt until a soft dough comes together.
Drop heaping Tablespoonfuls of dough into each muffin cavity using a cookie dough scoop. Flatten the dough slightly with your fingers. Bake for approx. 12-15 minutes or until the tops appear set and are slightly sunken in. Immediately upon removing from the oven, nestle a peppermint kiss candy in the center of each cup. Cool for about 15 minutes in the pan, then gently release them by running a knife along the outer edge and popping them out. If they resist at the 15 minute mark, allow them to cool a little longer in the pan. Cool the cups on a wire rack completely.
Clean out your stand mixer bowl and paddle attachment. To make your cheesecake frosting, beat together the butter, cream cheese, vanilla and peppermint extract until combined. Add in powdered sugar, about a cup at a time, until frosting is thick but fluffy. If the cheesecake frosting it too thick, stream in a little bit of milk to help thin it out some.
Pipe the cheesecake frosting onto the cookie cups, then immediately garnish with crushed candy cane pieces. Serve immediately, or store leftovers covered in the fridge.