Preheat your oven to 350°F (175°C). In a medium bowl, combine graham cracker crumbs, sugar, and melted butter until well mixed. Press this mixture firmly into a 9-inch springform pan to form an even crust. Bake in the oven for 10 minutes, then remove and allow it to cool completely before adding the filling.

In a large mixing bowl, beat the cream cheese with an electric mixer on medium speed until creamy and smooth, about 2 minutes. Gradually add the sugar and continue mixing until incorporated. Add eggs one at a time, mixing on low just until combined. Then, fold in the melted white chocolate, sour cream, peppermint extract, and vanilla extract until the filling is silky and free of lumps.

Pour the luscious filling over the cooled crust in the springform pan. Bake in the preheated oven for 50-60 minutes, until the edges are set and the center jiggles slightly when gently shaken. Turn off the oven, crack the door, and let the cheesecake cool inside for an additional hour to prevent cracking.

Carefully remove the cheesecake from the oven and allow it to cool to room temperature. Once cooled, refrigerate the cheesecake for at least 4 hours, preferably overnight, to set fully. When ready to serve, sprinkle the top with crushed peppermint candies.