Preheat the oven to 350F.
Whisk together the flour, baking powder and salt.
Mix the sugars in the melted butter.
Add the eggs to the butter-sugar mixture one at a time, beating after each addition.
Add the flour mixture to the butter-sugar-egg mixture and stir until well-blended. The mixture will be thick. Pour in the vanilla extract and mix to blend.
Transfer half of the batter to another mixing bowl. Into one portion, stir in the cocoa powder.
Using two ice cream scoops of the same size, drop the two batters alternately into a 5"x9" baking pan forming a chess board pattern. Dip a pointed knife into the batter on one corner of the pan, drag to the opposite end, make a U-turn to return to the opposite direction... do this until you have covered the entire pan. Turn the pan 45 degrees and repeat.
Bake in a preheated350F oven for 30 to 40 minutes or until a skewer inserted at the center comes out dry but with a few fine crumbs clinging to it.
Place the baking pan on a wire rack and cool completely.
Cut the brownies into two-inch squares (or larger, if you prefer) and serve.