Preheat your oven to 350°F (175°C). In a mixing bowl, combine graham cracker crumbs, sugar, and melted butter until fully moistened. Firmly press this mixture into the bottom of a springform pan to create an even layer. Bake for 10 minutes, then remove from the oven and allow it to cool completely while you prepare the filling.

In a large mixing bowl, beat the cream cheese until it's smooth and creamy, about 2 minutes. Gradually add granulated sugar, mixing until combined. Add the eggs one at a time, ensuring each is well incorporated before adding the next. Stir in the melted white chocolate, sour cream, peppermint extract, and vanilla extract, mixing until everything is silky and fully blended.

Pour the luscious cheesecake filling over the cooled crust, spreading it evenly with a spatula. Place the springform pan in the oven and bake for 50-60 minutes. Look for the edges to be set with a slight jiggle in the center. Once done, turn off the oven, leaving the cheesecake inside for an additional hour to cool gradually.

After the cheesecake has cooled to room temperature, cover it and refrigerate for at least 4 hours, or overnight for optimal flavor. When you're ready to serve, carefully remove the cheesecake from the springform pan. Garnish with crushed peppermint candies for a festive touch and a delightful crunch atop your White Chocolate Peppermint Cheesecake.