Do not preheat the oven yet. Line a 9 inch square metal pan with parchment paper or nonstick foil.
In a large, microwave-safe mixing bowl, combine the butter and both chocolates. Microwave on high for 30 seconds. Stir well. Continue microwaving at 50% power and stirring every 30 seconds until mixture is melted and smooth.
Add both sugars, salt and vanilla to the mixture and stir well. Stir in the eggs, one by one. Add the cake flour and stir until blended. Do not beat.
Spread mixture across the bottom of the pan and put in the freezer for 1 hour.
Preheat oven to 325 degrees F.
Melt the white chips in a small microwave-safe bowl using 50% of power and stirring every 30 seconds. Alternatively, you can melt them in a bowl set over but not touching simmering water. Let them cool slightly.
In a large mixing bowl, beat the cream cheese and sugar until well mixed, scraping sides of bowl. Beat in vanilla and melted white chips. Add the eggs and stir just until mixed.
Remove the brownie batter from freezer (it should be firm and very cold, but not a solid ice brick) and spread the cheesecake mixture over the top.
Drop about 10 teaspoons of raspberry preserves over cheesecake mixture and drag a knife through to make swirls.
Bake on center rack at 325F for about 45 to 50 minutes. The cheesecake should appear set around the edges, but jiggly in the center. It will set up and as cools, so don’t be tempted to overbake.
Let the brownies cool completely, then transfer to the refrigerator and chill overnight.
Grasp parchment paper, lift from pan and cut the brownies into squares.