Preheat oven to 350 degrees Fahrenheit. Grease a 9 x 13" cake pan.
In a mixing bowl, cream together cream cheese and 1/2 cup sugar. Add 2 eggs and 1 teaspoon vanilla, combine thoroughly. Set aside.
In a separate bowl, mix vegetable oil and 2 cups sugar. Add 4 eggs and 2 teaspoons vanilla, combine thoroughly.
In a separate bowl, sift together flour, baking powder, salt, and cocoa powder.
Add dry ingredients to oil, sugar, and egg mixture from step 4. Combine well. Spread brownie batter in a greased 9 x 13" cake pan.
Spoon dollops of cream cheese mixture on top of brownie batter. Use a knife to swirl the cream cheese mixture into the brownie mixture, creating a marbled look
Bake for 30 - 35 minutes or until brownies are set in the center and a knife inserted halfway between edge and center comes out clean.
Cool brownies on a wire rack for 15 minutes before cutting.