Preheat your oven to 350°F (175°C). Line a muffin tin with cupcake liners.
In a mixing bowl, combine the flour, sugar, cocoa powder, baking powder, baking soda, and salt. Whisk to combine.
Add the eggs, milk, vegetable oil, vanilla extract, and peppermint extract to the dry ingredients. Mix well using an electric mixer or whisk until fully combined.
Carefully add the boiling water to the batter. Mix until smooth; the batter will be thin.
Pour the batter evenly into the lined muffin tin, filling each cup about two-thirds full.
Bake in the preheated oven for 15-18 minutes or until a toothpick inserted into the center of a cupcake comes out clean. Let cool on a wire rack.
While the cupcakes cool, prepare the peppermint frosting. In a clean mixing bowl, beat the softened butter until creamy.
Gradually add the powdered sugar and mix until well combined. Add milk and peppermint extract, mixing until the frosting is smooth and fluffy.
Once the cupcakes are completely cooled, frost them using a piping bag or a knife.
Sprinkle crushed peppermint candies on top for decoration.