Preheat your oven to 325°F (160°C). Grease the sides of a 9-inch springform pan with butter or non-stick spray.
In a mixing bowl, combine the chocolate graham cracker crumbs and melted butter. Mix until the crumbs are well coated.
Press the crumb mixture into the bottom of the springform pan to form a firm crust. Bake in the preheated oven for 10 minutes, then remove and cool slightly.
In a large mixing bowl, beat the softened cream cheese with an electric mixer until smooth. Gradually add the granulated sugar and vanilla extract, mixing until well combined.
Add the eggs, one at a time, mixing on low speed after each addition until just incorporated. Do not overmix.
Stir in the melted semi-sweet chocolate and finely chopped pistachios gently with a rubber spatula.
Pour the cream cheese mixture over the cooled crust in the springform pan, smoothing out the top.
Bake in the preheated oven for 50-60 minutes, or until the center is set and a toothpick inserted comes out clean.
In the last 10 minutes of baking, prepare the topping by mixing sour cream and heavy cream together. Spread the mixture over the top of the cheesecake before taking it out of the oven.
Remove the cheesecake from the oven and let it cool at room temperature for at least an hour, then refrigerate for at least 4 hours or overnight for the best results.
Before serving, garnish the cheesecake with extra chopped pistachios.