Preheat the oven according to the instructions on your boxed brownie mix. Prepare the brownie batter as directed for an 8x8 inch pan. Grease a 9-inch springform pan thoroughly and pour the prepared batter into the bottom. Bake as directed on the package. Remove from oven and allow to cool slightly while preparing the cheesecake layer.

In a large mixing bowl, beat the softened cream cheese, granulated sugar, and vanilla extract with an electric mixer on medium speed until smooth and creamy. Add the sour cream and blend until fully incorporated.

Add the eggs one at a time, mixing on low speed just until combined after each addition. Avoid overmixing to prevent incorporating excess air.

Carefully pour the cheesecake mixture over the slightly cooled brownie base in the springform pan. Smooth the top with a spatula. If using a silver springform pan, bake at 325°F (163°C) for 60–65 minutes, or until the center is nearly set. If using a dark nonstick springform pan, reduce the oven temperature to 300°F (149°C) and bake for the same duration.

Once baking is complete, run a knife or metal spatula around the edge of the pan to loosen the cheesecake from the sides. Allow it to cool to room temperature, then refrigerate for at least 4 hours, or preferably overnight, before removing the springform ring and serving.