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1
To make the cupcakes: Preheat oven to 350 F. Line two cupcake pans with paper liners.
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2
In a medium bowl, whisk together the flour, cocoa powder, espresso powder, baking powder, baking soda and salt. Combine the milk, coffee and peppermint extract in a liquid measuring cup.
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3
In the bowl of a stand mixer fitted with the paddle attachment, beat the butter and sugars on medium-high speed until light and fluffy, about 3-4 minutes. Scrape down the sides of the bowl as needed. Add the eggs to the bowl, one at a time, letting the first incorporate fully before adding the second. With the mixer on low speed, alternately add the dry and wet ingredients, starting and ending with the dry ingredients. Mix only until everything is incorporated.
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4
Divide the batter evenly between the prepared cupcake liners. Bake for 18-20 minutes, or until a toothpick inserted in the center comes out clean. Let the cupcakes cool in the pan for about 5 minutes, then transfer them to a wire rack to cool completely.
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5
To make the frosting: In a heatproof bowl, stir the egg whites and sugar together. Set the bowl over a pan of simmering water. Heat, whisking frequently, until the mixture reaches 160 F and the sugar has dissolved. If you didn't use your stand mixer bowl to heat the mixture, transfer it to that bowl now. Fit your mixer with the whisk attachment. Beat the egg whites and sugar on medium-high speed until stiff peaks form and the mixture has cooled to room temperature, about 8-10 minutes. Reduce the mixer speed to medium and add the butter, 2 tablespoons at a time, adding more once each addition has been incorporated. If the frosting looks soupy or curdled, continue to beat on medium-high speed until smooth again, about 3-5 minutes more. Stir in the peppermint and vanilla extracts and mix just until incorporated.
