Prepare the brownie batter: Preheat the oven to 350°F and line an 8x8-inch pan with parchment paper. Melt the butter, then mix it with the brownie mix, eggs, vanilla, and cornstarch until smooth. Stir in chocolate chips. Pour ¾ of the batter into the pan, setting the rest aside.
Make the cheesecake layer: In a separate bowl, beat cream cheese, sugar, egg, and vanilla until smooth.
Layer and swirl: Spread the cheesecake mixture over the brownie batter. Drop spoonfuls of the reserved brownie batter on top, then swirl with a toothpick or knife.
Bake and cool: Bake for 35–40 minutes until the edges are set and the center slightly jiggles. Let cool completely before slicing.