Preheat the oven to 350°F (175°C). Grease a 9-inch springform pan or line it with parchment paper.
Prepare the brownie batter according to the package instructions and pour it into the prepared pan.
Bake for 20–25 minutes until the brownie layer is mostly set but not fully baked. Remove and let cool slightly.
In a large mixing bowl, beat the cream cheese and sugar until smooth.
Add eggs one at a time, mixing well after each addition. Mix in vanilla extract and sour cream.
Pour the cheesecake mixture over the slightly cooled brownie layer.
Bake for 40–45 minutes or until the center is almost set. Turn off the oven, crack the door open, and let the cheesecake sit for 1 hour.
Refrigerate for at least 4 hours or overnight before serving.