Prepare the crust:

Preheat the oven to 325°F (163°C). In a mixing bowl, combine the chocolate graham cracker crumbs, sugar, and melted butter. Stir until well combined. Press the mixture into the bottom of a 9-inch springform pan to form a firm crust. Bake for 10 minutes, then remove and allow it to cool.

Make the cheesecake filling:

In a large mixing bowl, beat the softened cream cheese with an electric mixer until smooth. Gradually add the sugar and continue mixing until fully incorporated. Stir in the vanilla extract.

Incorporate eggs:

Add the eggs one at a time, mixing on low speed until just combined. Be careful not to overmix to avoid introducing too much air into the batter.

Add sour cream and cream:

Mix in the sour cream and heavy cream until smooth and creamy.

Add chocolate:

Divide the cheesecake mixture evenly into three bowls. In one bowl, fold in the melted semi-sweet chocolate. In another, mix in the melted dark chocolate. In the third, stir in the melted white chocolate.

Layer the cheesecake:

Pour half of the semi-sweet chocolate mixture over the cooled crust. Layer with the dark chocolate mixture, followed by the white chocolate mixture. Top with the remaining semi-sweet chocolate mixture, creating a marbled effect if desired.

Bake the cheesecake:

Place the springform pan on a baking sheet and bake for 55-65 minutes, or until the edges are set but the center is slightly jiggly. Turn off the oven and let the cheesecake cool inside for 1 hour.

Chill:

Remove the cheesecake from the oven and let it cool to room temperature. Once cooled, refrigerate for at least 4 hours or overnight for best results.

Serve:

Before serving, top with whipped cream, shaved chocolate, and a drizzle of chocolate sauce. Slice and enjoy this indulgent treat!