01 - Preheat the oven to 350°F and line a 12-cup muffin tin with cupcake liners.
02 - In a large bowl, whisk together flour, cocoa powder, sugar, baking powder, baking soda, and salt until evenly mixed.
03 - In a separate bowl, beat eggs, milk, vegetable oil, vanilla extract, and peppermint extract until well blended.
04 - Pour the wet mixture into the dry ingredients and stir until just combined.
05 - Gradually whisk in the hot water until the batter is smooth and thin.
06 - Distribute batter evenly into the cupcake liners, filling each about two-thirds full.
07 - Bake for 18 to 20 minutes or until a toothpick inserted into the center comes out clean.
08 - Allow cupcakes to cool in the pan for 5 minutes, then transfer them to a wire rack to cool completely.
09 - Beat softened butter on medium speed until creamy. Gradually add powdered sugar, milk, peppermint extract, and a pinch of salt, beating until light and fluffy.
10 - Spread the frosting atop cooled cupcakes and optionally sprinkle with crushed peppermint candies.