Preheat your oven to 300°F (150°C).
In a medium bowl, gently combine the finely crushed mint cookies with the melted butter until everything is just moistened.
Lightly press this cookie mixture evenly onto the bottom of a 9-inch springform pan. Set it aside.
In a large mixing bowl, using an electric mixer, beat the softened cream cheese, granulated sugar, vanilla extract, and peppermint extract until the mixture is smooth and well blended. Remember not to overmix!
Carefully add the eggs, one at a time, mixing on low speed after each addition until just combined. Overbeating can make the cheesecake tough.
Gently stir in the 2 tablespoons of holiday sprinkles. Then, pour this delightful filling over your prepared cookie crust in the springform pan.
Bake for about 1 hour and 5 minutes, or until the edges look set but the center still has a slight, delicate jiggle. This means it's perfectly cooked!
Once baked, carefully run a thin knife around the rim of the pan to help loosen the cake as it cools. Let it cool completely on a wire rack, then transfer it to the refrigerator for at least 4 hours, or ideally overnight, to chill thoroughly.
In the bowl of an electric stand mixer, beat the softened butter until it's light and fluffy.
Slowly add the powdered sugar and ½ teaspoon of vanilla extract, mixing on low speed until smooth. If the frosting feels too thick, a tiny splash of milk can help thin it out.
Once your cheesecake is completely chilled, spread the buttercream frosting evenly over the top surface.
For a beautiful touch, you can pipe some of the frosting around the edge using a pastry bag and a star tip, if desired.
Finally, decorate your cheesecake with crushed mini candy canes, peppermint candies, and extra holiday sprinkles for a dazzling, festive presentation!
Slice, serve, and enjoy this easy and delicious holiday treat!