Preheat oven to 350 degrees. Grease an 8×8 or 9×9 glass baking dish with parchment paper.
Melt the butter and semi-sweet chocolate chips in the microwave in 30 second increments. Stir after each 30 seconds. Set aside.
Whisk together the flour, cocoa, salt and baking powder. Set aside.
Whisk the eggs and sugar together in a large bowl. Next add in the melted chocolate butter mixture and mix until combined. Gradually add in the dry ingredients and mix until combined.
In the microwave, in 30 second increments, melt the white chocolate chips. Stir after each 30 seconds.
Mix the cream cheese, egg and sugar and beat until smooth. Next stir in the melted white chocolate chips until well combined.
Pour half of the brownie batter into the prepared glass dish and spread evenly. Drop spoonfuls of the cheesecake mixture on top of the brownie batter. Spread with a knife. Top with the remaining brownie batter and spread evenly over the cheesecake mixture.
Take a knife and swirl the mixture around a bit. You want to run some of the cheesecake mixture through the brownie batter.
Bake for 45-50 minutes or until the brownie top crinkles and a toothpick inserted in the middle comes out clean.
Allow to cool a couple of minutes in the dish and then lift the parchment paper by the corners and let finish cooling on a baking rack. Make sure and let them cool completely before you cut into squares.