Beat cream cheese in a stand mixer until light and fluffy. Add sugar, flour, sour cream, and vanilla. Mix to combine.
Add eggs and beat until the mixture is smooth and all the ingredients are incorporated. Scrape the sides and the beater as needed.
Pour the batter over the brownie layer after the brownie layer has baked for 15 minutes.
Place on the middle rack of the oven. Add a pan, partially-filled with water, under the cheesecake. This "water-bath" allows the cheesecake to bake without cracking.
Bake for one hour, or until the cheesecake is no longer jiggly in the center. Cook longer as necessary, checking every five minutes, until done.
Remove the cheesecake from the oven, and allow it to come to room temperature on the counter.