Preheat your oven to 325°F (160°C).

In a medium bowl, combine the chocolate graham cracker crumbs, sugar, and melted butter. Mix until the crumbs resemble wet sand. Press this mixture firmly into the bottom of a 9-inch springform pan. Bake for about 10 minutes, then allow it to cool slightly.

In a large mixing bowl, beat the softened cream cheese until smooth. Add the granulated sugar, vanilla extract, and peppermint extract. Beat until everything is well combined.

Add the large eggs, one at a time, mixing after each addition. Then, fold in the sour cream and melted semi-sweet chocolate until the mixture is smooth.

Pour the filling over the cooled crust and smooth the top gently. Bake for 55 to 65 minutes, or until the edges are set and the center is slightly jiggly.

Once baked, turn off the oven and crack the door open, allowing the cheesecake to cool inside for about an hour. Then transfer it to the refrigerator for at least 4 hours, or overnight.

When ready to serve, top with whipped cream, shaved chocolate, and fresh mint leaves.