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Preheat the oven to 350 F. Place freestanding cupcake wrappers on a baking sheet.
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In a large bowl, combine sugar, flour, baking powder, baking soda, salt, and black cocoa powder.
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Add egg, milk, oil, and vanilla. Beat on medium speed until combined, about 2 minutes.
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Stir in boiling water. Batter will be thin and runny.
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Pour batter into the prepared baking cups, filling each cup about ½ -⅔ full.
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Bake cupcakes for 15 minutes or until a toothpick inserted into the center comes out clean.
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Cool the cupcakes on the baking sheet for 10 minutes before transferring to a wire rack to cool completely.