1. Preheat the oven to 325°F and lightly grease a 9-inch springform pan.

2. Mix the crushed chocolate sandwich cookies with the melted butter until the crumbs are evenly coated.

3. Press the crust mixture firmly into the bottom of the springform pan and bake for 8 to 10 minutes. Let it cool.

4. Beat the cream cheese until smooth, then mix in the granulated sugar and sour cream.

5. Add the eggs one at a time, mixing on low speed just until combined, then stir in the vanilla extract.

6. Divide the cheesecake batter evenly between two bowls.

7. Stir the melted semi-sweet chocolate and cocoa powder into one bowl to make the chocolate layer.

8. Stir the peppermint extract into the second bowl to make the peppermint layer.

9. Pour the chocolate batter over the cooled crust and smooth the top.

10. Gently spread the peppermint batter over the chocolate layer.

11. Bake for 55 to 65 minutes until the edges are set and the center still slightly jiggles.

12. Turn off the oven, crack the oven door, and let the cheesecake rest inside for 1 hour.

13. Remove the cheesecake and cool completely at room temperature.

14. Refrigerate for at least 6 hours or overnight.

15. Whip the heavy cream with the powdered sugar until soft peaks form.

16. Top the chilled cheesecake with whipped cream, crushed candy canes, and chocolate shavings before serving.