Preheat the oven to 350 degrees F. Line an 8 or 9 inch square pan with parchment paper, leaving an overhang of parchment on both sides. Coat the parchment lined pan with cooking spray.
For the brownies: Place the butter and 1 1/3 cups of chocolate chips into a large bowl. Microwave in 30 second increments until just melted. Stir until smooth.
Let the chocolate mixture cool for 5 minutes. Whisk in the sugar, then whisk in the eggs, one by one. Finally, whisk in the vanilla extract.
Add the flour, cocoa powder and salt to the bowl. Stir gently until just combined.
Reserve 1/4 of of the brownie batter in a separate bowl.
Fold the remaining chocolate chips into the larger amount of the brownie batter.
Spread the larger amount of batter evenly into the prepared pan.
For the cheesecake filling: Place the cream cheese and sugar in a bowl. Beat with a mixer for 2-3 minutes or until smooth and creamy. Add the egg and vanilla extract, then beat until smooth.
Pour the cheesecake mixture over the brownie batter in the pan.
Add 1 tablespoon of very hot water to the reserved brownie batter. Stir until smooth.
Dollop the brownie batter over the cheesecake. Use a skewer or knife to swirl the two batters together.
Bake for 30-35 minutes or until a toothpick inserted into the center of the brownies comes out clean or with just a few crumbs attached.
Cool the brownies completely.
Use the parchment overhang to lift the brownies out of the pan. Cut into squares, then serve.