Preheat the oven to 350°F (175°C).
Grease a 9-inch springform pan with butter.
Melt the butter in a medium saucepan over low heat.
Stir in the granulated sugar and brown sugar until well combined.
Add the eggs, one at a time, blending after each addition.
Stir in vanilla extract and cocoa powder, then mix in flour until just combined.
Pour the brownie batter into the prepared springform pan and spread evenly.
Bake for 20-25 minutes or until a toothpick inserted comes out with a few moist crumbs.
While the brownie bakes, prepare the cheesecake mixture. Beat cream cheese with an electric mixer until smooth.
Add sugar, sour cream, and vanilla extract, mixing until smooth.
Pour the cheesecake mixture over the baked brownie layer.
Bake for an additional 35-40 minutes. The cheesecake should be set but slightly jiggly in the center.
Allow the cheesecake to cool completely in the pan, then refrigerate for at least 4 hours, preferably overnight.
Before serving, melt the hot fudge sauce and drizzle over slices as desired, topped with whipped cream and optional nuts.