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For the brownies: Preheat the oven to 350 degrees F. Grease a 9- by 13-inch baking pan with butter.
Mix together the sugar, butter, cocoa, flours, vanilla, baking powder, salt and eggs with an electric mixer or by hand until smooth. Pour into the greased pan. Pour the peanut butter topping in three vertical lines over the brownies. Draw a butter knife horizontally through the lines, creating a marbling effect. Bake the brownies until a toothpick inserted in the center comes out clean, 35 to 45 minutes.