Prepare the Crust
Preheat your oven to 350°F (175°C). In a medium bowl, combine the chocolate wafer crumbs, melted butter, and sugar. Press the mixture firmly into the bottom of a 9-inch springform pan. Bake for 8-10 minutes, or until the crust is set. Let cool completely.
Make the Filling
In a large bowl, beat the cream cheese and sugar until smooth and creamy. Beat in the sour cream, heavy cream, and vanilla extract until well combined. Gradually beat in the melted white chocolate until smooth. Stir in the peppermint extract.
Create the Swirls
Divide the cheesecake batter in half. In one bowl, add a few drops of red food coloring and gently mix until you achieve your desired color. Alternate spoonfuls of the white and red batter into the prepared crust. Use a knife or skewer to swirl the batters together, creating a marbled effect. Be careful not to overmix!
Bake the Cheesecake
Wrap the bottom of the springform pan tightly with aluminum foil to prevent water from seeping in. Place the springform pan inside a larger roasting pan. Pour hot water into the roasting pan until it reaches about halfway up the sides of the springform pan (this is a water bath). Bake for 60-75 minutes, or until the edges are set but the center still has a slight jiggle. Turn off the oven and let the cheesecake sit in the oven with the door slightly ajar for 1 hour. This gradual cooling helps prevent cracking.
Chill and Garnish
Remove the cheesecake from the water bath and let it cool completely on a wire rack. Cover the cheesecake with plastic wrap and chill in the refrigerator for at least 6 hours, or preferably overnight. Before serving, remove the cheesecake from the springform pan and garnish with crushed peppermint candies (optional).