Mash the raspberries in a small bowl with sugar and cornstarch until no white remains.
Assemble. Spread the brownie batter (minus the reserved 1/2 cup) evenly into the prepared pan. Pour the cheesecake mixture over the brownie batter and spread into an even layer.
Drop the reserved brownie batter in rough vertical lines across the cheesecake layer. Add the raspberry mixture between the brownie batter lines, leaving any excess liquid in the bowl. Use a skewer or knife to swirl horizontally across the lines to create a marbled effect. Top with extra chocolate chips and a few whole raspberries if desired.
Bake for 38-42 minutes, or until the edges are set and the center has a slight jiggle.
Cool the brownies completely in the pan, then refrigerate for at least 1 hour before removing from the pan and slicing.