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Preheat the oven to 375 F. Line muffin pan with cupcake liners.
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Whisk cocoa powder into boiling water. Set aside to cool.
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In a small bowl, combine the flour, baking powder, and salt. Set aside.
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In a medium bowl, beat the butter and sugar until light and fluffy.
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Add the egg and vanilla and beat until well-mixed. Stir in the cocoa mixture.
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Add the flour mixture and beat until combined.
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Scoop the batter into the prepared muffin pan and bake for 15-18 minutes, or until a toothpick inserted in the center comes out clean.
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Let the cupcakes cool completely before frosting.