Preheat your oven to 350°F (175°C). Line an 8x8 inch baking pan with parchment paper, leaving an overhang on two sides.
Melt the butter in a large microwave-safe bowl, then whisk in the cocoa powder until smooth. Add the sweetened condensed milk and vanilla and whisk until thick and glossy.
Sprinkle the flour, baking powder and salt over the mixture and fold until no dry spots remain, then fold in the chocolate chips. Set aside 1/2 cup of the batter and spread the rest evenly into the prepared pan.
In a medium bowl, beat the cream cheese and sugar with a hand mixer for about 2 minutes, until completely smooth with no lumps. Beat in the sour cream, flour and vanilla just until combined.
Spread the cheesecake mixture over the brownie batter in an even layer. Drop small spoonfuls of the reserved brownie batter on top, then drag a toothpick through to create a marbled pattern.
Bake for 30 to 35 minutes, until the edges are set and the cheesecake layer looks set with only a slight wobble in the very center. The cheesecake should stay mostly pale.
Cool in the pan for 1 hour, then refrigerate for at least 3 hours or overnight.Chilling is what gives the cheesecake layer its creamy, sliceable texture. Cut into 16 squares, wiping clean between cuts for neat layers.