Heat the oven to 350 F and spray a 9x13 baking pan with non-stick cooking spray.
Begin by preparing the base. In the bowl of a mixer combine the flour, cocoa, baking power, baking soda, salt, and sugar until well mixed.
Add the melted butter, both eggs, and vanilla and mix until a stiff dough forms. Turn the dough out into the prepared pan and press it so it covers the pan evenly. Set aside.
In a medium bowl cream together the butter and cream cheese until smooth and evenly mixed. Add the eggs, one at a time, mixing well after each. Next add the vanilla, powdered sugar and melted white chocolate and mix until thoroughly combined.
Pour the topping over the base and spread it so it is even.
Bake for 35 to 45 minutes, or until the top is browned and the center is just slightly jiggly. Cool at room temperature for one hour then chill in the refrigerator until very cold, at least 2 hours or overnight. Cut the cake into desired number of pieces and dust with powdered sugar just before serving.
For presentation, drizzle plates with chocolate syrup or hot fudge.