Spray a 9-inch springform pan with cooking spray, and line the bottom with parchment paper.
Make the Brownie Base
Mix 1 18-oz box brownie mix, 1 of the 3 large eggs, ⅓ cup oil, and ¼ cup water in a medium bowl until combined. (Follow the ingredients on whichever box of brownie mix you have. This is what is on the box I had.)
Pour the brownie batter in the prepared springform pan and bake for 15 minutes. It will not be fully cooked, and should still be jiggly. This is fine.
Make the Cheesecake Filling
While the brownie layer is baking, use an electric mixer or a stand mixer with the paddle attachment to blend 1 lb softened cream cheese, 1 tablespoon all-purpose flour, ¾ cup white sugar, and ¼ cup sour cream and 1 teaspoon vanilla extract in a large bowl until smooth.
Mix in the remaining 2 3 large eggs, one at a time until each egg is fully incorporated, but do not over-mix. The cheesecake filling should be smooth and wet.
When the brownie layer is done, reduce the temperature of the oven to 325°F.
Open the oven for a couple of minutes to make sure it cools down enough before putting the cheesecake back in.
Spoon the cheesecake filling on top, around the edges first then in the middle, while the brownie layer is still hot and wobbly.
Bake
Bake the cheesecake for 40-45 minutes or until the cheesecake is set around the edges but the center still jiggles a little. Turn off the oven and let the cheesecake sit in the oven for 1 hour, with the door cracked.
After an hour, the cheesecake should be firm and set.
Let the cheesecake rest on a cooling rack for another 1 hour or until it is room temperature before covering it with plastic wrap and placing it in the fridge for at least another 4 hours.
Serve
When you are ready to serve, carefully remove the outside ring of the springform pan, and remove the parchment paper from the bottom.
Transfer the cheesecake to a platter or cake stand, garnish with chocolate syrup or whipped cream, optional, and serve chilled.
Notes
For the brownie layer - follow the instructions for the batter on the box. Mine has eggs, oil and water. But if yours is different, follow those instructions.