1. Preheat the oven to 350°F (175°C) and line a 12-cup muffin tin with festive liners.

2. Whisk together flour, cocoa powder, baking powder, baking soda, and salt in a bowl until smooth.

3. Cream the butter and sugar in a separate bowl until pale and fluffy.

4. Beat in the eggs one at a time, then mix in the brewed espresso and peppermint extract.

5. Alternate adding the dry ingredients and milk, mixing just until combined to avoid overmixing.

6. Divide the batter evenly among the liners, filling each two-thirds full.

7. Bake for 18–20 minutes or until a toothpick comes out clean, then cool in the tin for five minutes.

8. Transfer cupcakes to a wire rack and let cool completely before frosting.

9. Beat softened butter until light, then gradually add powdered sugar, heavy cream, and peppermint extract until smooth.

10. Pipe or spread the frosting on cooled cupcakes and sprinkle with crushed candy canes before serving.