Preheat your oven to 350°F (175°C). In a mixing bowl, combine graham cracker crumbs, sugar, and melted butter until thoroughly mixed. Firmly press this mixture into the bottom of a 9-inch springform pan to create a sturdy crust. Bake for 10 minutes, then let it cool to room temperature.

In a large bowl, beat the softened cream cheese with an electric mixer on medium speed until smooth and creamy, about 2-3 minutes. Gradually add granulated sugar, mixing until fully combined. Incorporate the eggs one at a time, ensuring each is well blended before adding the next.

Gently fold in melted white chocolate, sour cream, peppermint extract, and vanilla extract. Mix on low speed just until well combined.

Pour the filling into the cooled graham cracker crust, spreading it evenly. Bake in the preheated oven for 50-60 minutes, until edges are set but the center is slightly jiggly. Turn off the oven and leave the cheesecake inside for an hour to cool gently.

Let the cheesecake cool to room temperature, cover loosely, and chill in the refrigerator for at least 4 hours, preferably overnight. Before serving, sprinkle crushed peppermint candies on top.