Preheat your oven to 325°F (163°C). Line a 9-inch springform pan with parchment paper and grease the sides lightly.

Melt ½ cup of butter in a medium saucepan over low heat, then stir in both sugars until combined. Add in beaten eggs and vanilla extract, then mix in flour, cocoa powder, and salt.

Spread the brownie batter in the prepared pan and bake for 20-25 minutes. Remove and let cool slightly.

In a large bowl, beat cream cheese and sour cream until smooth. Gradually mix in sugar, then add eggs one at a time followed by flour until just combined.

Pour the cheesecake filling over the cooled brownie base, smoothing the top.

Bake for an additional 40-45 minutes until the edges are set but the center is slightly jiggly. Leave in the oven with the door ajar to cool.

After cooling for an hour, chill in the refrigerator for at least 4 hours or overnight.

When ready to serve, release the sides of the pan, slice with a clean knife, and serve chilled, optionally garnished with whipped cream or berries.