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Preheat oven to 350 degrees.
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Prepare an 8-inch square baking pan by buttering the pan, then lining with parchment paper. Leave a few inches of paper on either side to lift out the brownies later. Then, butter the parchment paper.
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In a double boiler, combine butter, chocolate and cocoa until melted. Remove from heat and let cool slightly.
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Whisk together flour, baking powder and salt. Set aside.
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With an electric mixer, combine sugar, eggs and vanilla with the whisk attachment. Mix on medium speed until the mixture is a pale yellow, about 3-4 minutes. Add chocolate mixture and mix to combine. Reduce speed and add flour mixture until combined.
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Pour batter into prepared pan and smooth evenly. Bake for 35 minutes or until toothpick comes out clean, with a few crumbs, but not wet.
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Let cool 15 minutes in pan, then transfer to cooling rack to cool completely.