Preheat your oven to 300°F (150°C). In a bowl, combine crushed mint Oreo cookies with melted butter and press evenly into a 9-inch springform pan. Bake for 10 minutes and let it cool.

In a mixing bowl, beat the cream cheese, granulated sugar, vanilla extract, and peppermint extract until smooth. Gradually add the eggs, mixing on low speed until just blended.

Fold in holiday sprinkles into the cheesecake mixture, then pour over the cooled crust. Bake for 1 hour and 5 minutes. The center should be slightly jiggly.

Turn off the oven and leave the cheesecake inside for 10 minutes. Once cooled, refrigerate for at least 4 hours.

While chilling, beat the softened butter until fluffy, slowly adding confectioners' sugar until smooth. Adjust with milk for desired consistency.

Remove the cheesecake from the springform pan, spread buttercream frosting on top, and decorate with mini candy canes and sprinkles.