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Preheat oven to 350°F. Line a standard muffin pan with paper cupcake liners.
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Make the cupcakes: In a large bowl, whisk together the flour, cocoa powder, baking powder, baking soda, sugar, and salt together.
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In the bowl of stand mixer or using a hand mixer, beat together the egg, milk, oil, peppermint, and vanilla. Slowly add the flour mixture and beat on medium speed with an electric mixer for 30 seconds. Scrape down the sides of the bowl and continue mixing on medium speed for 1 to 2 minutes. Add boiling water and stir to combine.
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Divide the batter equally into prepared muffin tin filling to about three-quarters full. Bake for 18-20 minutes or tops are firm and a cake tester inserted in the center comes out clean Remove pan from oven and allow cupcakes to cool in pan for 10 minutes. Remove cupcakes from pan and let cool completely before frosting.
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Meanwhile, make the frosting: Beat softened butter with a hand or stand mixer on medium speed. Beat for about 3 minutes until smooth and creamy.
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Add powdered sugar and mix until combined.
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Add eggnog, cinnamon, nutmeg and mix until smooth.
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If necessary, add more eggnog or powdered sugar until desired consistency is reached.
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Frost cooled cupcakes. Drizzle with melted chocolate. Top with crushed candy canes and crushed Andes Peppermint Crunch Thins right before serving.