Preheat your oven to 325°F (160°C). Grease and line a 9-inch springform pan with parchment paper.
In a medium bowl, mix melted butter and sugar until combined.
Beat in eggs and vanilla extract.
Stir in cocoa powder, flour, and salt until just combined.
Spread brownie batter evenly in the bottom of the prepared pan.
Bake for 20 minutes. Remove from oven and let cool slightly.
Meanwhile, prepare the cheesecake layer: Beat cream cheese until smooth.
Add sugar and vanilla and beat until combined.
Add eggs one at a time, mixing on low speed until just incorporated.
Mix in sour cream until smooth.
Pour cheesecake batter over the cooled brownie layer.
Place the springform pan on a baking sheet and bake for 45-50 minutes, or until the center is almost set but still slightly jiggly.
Turn off the oven, crack the door, and let the cheesecake cool in the oven for 1 hour.
Remove from oven and refrigerate for at least 6 hours or overnight.
Before serving, run a knife around the edges and remove the springform.