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Preheat oven to 375°F and prepare an 8-inch round baking pan. Butter the pan and line the bottom with a round of wax paper. Butter paper bottom, as well.
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Chop chocolate into small pieces.
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Put chocolate and butter in a glass bowl or large-capacity measuring cup.
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Microwave butter and chocolate together in 30 second intervals until melted, stirring after each interval.
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Whisk sugar into chocolate mixture.
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Add eggs and whisk well.
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Sift 1/2 cup cocoa powder over chocolate mixture and whisk until just combined. Pour batter into pan and bake in middle of oven 25 minutes, or until top has formed a thin crust. Cool cake in pan on a rack 5 minutes and invert onto a serving plate.
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Place desired stencil on cake and sift powdered sugar over cake. Serve.