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To make the cupcakes: Preheat oven to 350 degrees F.
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Whisk together flour, baking powder, and salt in a bowl.
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Beat together peanut butter, butter, and brown sugar in a large bowl with an electric mixer at medium speed until blended, about 2 minutes.
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Add egg and vanilla and beat until fluffy, about 1 minute.
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Reduce speed to low and add flour mixture and milk alternately in batches, beginning and ending with flour mixture, then mix until just combined.
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Divide batter among lined muffin cups (about two-thirds full) and bake in middle of oven until pale golden and a tester inserted in center of a cupcake comes out clean, 18 to 20 minutes.
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Turn cupcakes out onto a rack and cool completely.
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To make the Icing while cupcakes cool: Bring cream to a boil in a small saucepan, then pour over chocolate in a small bowl.
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Let stand 1 minute, then whisk until smooth.
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To thicken icing to spreading consistency quickly, spread it on a metal baking sheet and chill until thick and glossy, about 5 minutes.
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Scrape icing back into bowl and stir until smooth.
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Spread icing on cupcakes and sprinkle with peanuts.
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Cooks' notes:
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* If you aren't pressed for time, chill icing in bowl, uncovered, stirring occasionally, 20 to 30 minutes before spreading on cupcakes.
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* Iced cupcakes keep, chilled in an airtight container, 3 days.