Preheat oven to 350°F (or as directed on the brownie mix box).
Grease a 9x9 or 8x8-inch baking pan, or line it with parchment paper.
Prepare the brownie mix as directed, adding the chocolate chips once the batter has been mixed.
Spread about ¾ of the batter into the pan in an even layer.
Prepare the cheesecake layer by beating the cream cheese, sugar, egg, and vanilla in a mixing bowl until smooth.
Spread the cheesecake mixture over the brownie batter in a smooth, even layer.
Drop tablespoonfuls of the remaining brownie batter on top of the cheesecake layer, don’t spread it out. Drag a knife or a toothpick through the batter to swirl it through the cheesecake layer.
Bake for 35–40 minutes, or until a toothpick inserted near the center comes out with a few moist crumbs.