Preheat the oven to 350°F (175°C). Grease a 9-inch springform pan and line the bottom with parchment paper.
Prepare the brownie batter according to the package directions using the oil, water, and 2 eggs listed above (or follow the package instructions if they differ).
Pour the brownie batter into the prepared pan and bake for 15 minutes until the top is just set.
Meanwhile, beat the softened cream cheese until smooth and fluffy.
Add the granulated sugar and beat until fully combined.
Mix in the flour, vanilla extract, sour cream, and ¼ cup heavy cream until smooth.
Stir in one egg by hand until incorporated, then gently mix in the remaining egg.
Pour the cheesecake mixture over the partially baked brownie layer.
Reduce the oven temperature to 325°F (163°C).
Bake the Brownie Bottom Cheesecake for 45 minutes.
Turn off the oven and leave the door closed for 20 minutes.
Crack the oven door open slightly and allow the cheesecake to cool inside for another 30 minutes.
Cool completely at room temperature, then refrigerate for 2–3 hours or overnight.
Before serving, whip the remaining heavy cream with powdered sugar until stiff peaks form.
Spread or pipe the whipped cream over the cheesecake and drizzle generously with hot fudge sauce or chocolate ganache.