Preheat your oven to 350°F (175°C) and grease a 9-inch springform pan. In a microwave-safe bowl, melt ½ cup of butter until bubbly. Stir in 1 cup of sugar and ½ cup of cocoa powder until fully combined. Add in 2 room temperature eggs, mixing until smooth, then incorporate ½ cup of flour just until no dry streaks remain.

Pour the brownie batter into the prepared springform pan, spreading it evenly with a spatula. Bake in the preheated oven for 20-25 minutes, until the edges are set and a toothpick inserted in the center comes out with a few moist crumbs. Remove from the oven and allow the brownie base to cool completely in the pan on a wire rack.

While the brownie cools, beat 16 ounces of softened cream cheese in a mixing bowl until smooth and creamy with an electric mixer. Gradually add ½ cup of sugar, then blend in ¼ cup of sour cream, 2 eggs, and 1 teaspoon of vanilla extract. Mix until the cheesecake batter is light and completely smooth, ensuring no lumps remain.

Once the brownie base is fully cooled, pour the cheesecake mixture over the top, spreading it gently to cover the surface. Set the springform pan inside a larger baking dish filled with hot water, creating a water bath to help regulate temperature. Bake in the oven for 50-60 minutes, or until the cheesecake is set around the edges but slightly jiggly in the center.

After baking, turn off the oven and crack the door open, allowing the cheesecake to cool slowly for about 1 hour to prevent cracking. Once at room temperature, transfer it to the refrigerator to chill for at least 4 hours, but ideally overnight.

When ready to serve your Brownie Cheesecake, carefully remove it from the springform pan. Garnish with whipped cream or fresh berries, slice into generous portions, and enjoy!