Preheat your oven to 350°F (175°C). In a large mixing bowl, combine graham cracker crumbs, sugar, and melted butter until evenly mixed. Pour into a springform pan, pressing down firmly to form a compact crust. Bake for 10 minutes or until golden brown, then set aside to cool.

In a separate mixing bowl, beat the cream cheese with an electric mixer on medium speed until smooth and creamy, about 3-4 minutes. Gradually add granulated sugar, then incorporate the eggs one at a time until fully blended.

Melt the white chocolate in a microwave-safe bowl and mix it into the cream cheese filling along with sour cream, peppermint extract, and vanilla extract. Stir until well combined.

Pour the filling over the cooled crust in the pan, spreading evenly. Bake for 50-60 minutes until the edges are set, with a slight jiggle in the center. Turn off the oven and let the cheesecake cool inside with the door slightly ajar for about an hour.

After cooling, refrigerate for at least 4 hours or overnight. When ready to serve, remove from the pan and top with crushed peppermint candies.