Preheat your oven to 350°F (175°C) and grease the cake pans with butter or non-stick spray.
In a large mixing bowl, combine the flour, sugar, cocoa powder, baking powder, baking soda, and salt. Mix well.
Add the eggs, milk, vegetable oil, and peppermint extract to the dry ingredients. Mix until well combined.
Carefully stir in the boiling water (the batter will be thin). Mix until silky smooth.
Pour the batter evenly into the prepared cake pans.
Bake for 30 minutes, or until a toothpick inserted in the center comes out clean. Let the cakes cool in the pans for 10 minutes, then turn them out onto a cooling rack to cool completely.
While the cakes are cooling, prepare the frosting. In a mixing bowl, beat the softened butter until creamy. Gradually add the powdered sugar, mixing until combined.
Stir in the peppermint extract and heavy cream. Beat on high speed for 2-3 minutes until the frosting is light and fluffy. Add more cream if needed to reach desired consistency.
Once the cakes are completely cool, place one layer on a serving plate. Spread a layer of frosting on top, then place the second layer on top.
Frost the top and sides of the cake with the remaining peppermint frosting. If desired, decorate the top with crushed peppermint candies.
Slice and serve the peppermint cake.