Preheat your oven to 325°F.

In a large mixing bowl, beat the softened cream cheese with an electric mixer until smooth. Gradually add the granulated sugar and continue to mix until well combined.

Add the vanilla extract and eggs, one at a time, mixing well after each addition. Stir in the sour cream until the mixture is creamy and smooth.

In a microwave-safe bowl, melt the semi-sweet chocolate chips in 30-second intervals, stirring in between until completely melted. Once melted, mix in the cocoa powder and milk until smooth.

Pour half of the cream cheese mixture into the prepared graham cracker crust. Drizzle half of the chocolate mixture over the cream cheese layer. Use a knife or skewer to swirl the chocolate into the cream cheese layer.

Pour the remaining cream cheese mixture on top, followed by the rest of the chocolate mixture. Swirl again to create a marbled effect.

Bake in the preheated oven for 50-60 minutes, or until the center is set but still slightly jiggly. Turn off the oven and leave the cheesecake inside for an additional hour to cool gradually.

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