Heat the oven to 350°. Coat a 9-inch square baking pan with cooking spray. In a medium bowl with a hand mixer set on medium speed, blend the first five cheesecake ingredients until smooth. Blend in the flour. Set the batter aside.
In a large heat-safe bowl, microwave the chocolate chips and butter in 25-second bursts, whisking thoroughly after each one, until the mixture is melted and smooth (two to three times). Add the eggs, sugar, and vanilla extract, and whisk to incorporate. Stir in the remaining ingredients.
Evenly spread the brownie batter in the pan. Layer on the cheesecake batter, then use a butter knife or small spatula to swirl the batters. Bake until a toothpick inserted in the center comes out clean, about 30 minutes. Let cool before cutting.