Preheat your oven to 350°F (175°C). Grease and flour two 9-inch round cake pans.
In a large mixing bowl, sift together the flour, sugar, cocoa powder, baking powder, baking soda, and salt.
Add the eggs, milk, vegetable oil, and vanilla extract to the dry ingredients. Beat on medium speed for 2 minutes until well combined.
Carefully stir in the boiling water; the batter will be thin. Mix until smooth.
Divide the batter evenly between the prepared cake pans.
Bake for 30 to 35 minutes or until a toothpick inserted into the center comes out clean.
Remove the cakes from the oven and allow them to cool in the pans for 10 minutes.
Turn the cakes out onto wire racks and cool completely.
To make the frosting, beat the softened butter on medium speed until creamy, about 2 minutes.
Gradually add the powdered sugar and cocoa powder, beating on low speed until combined.
Add the milk and vanilla extract and beat on high speed for 3 minutes until the frosting is light and fluffy.
Place one cake layer on a serving plate. Spread a thick layer of frosting evenly over the top.
Place the second cake layer on top and frost the top and sides of the cake with the remaining frosting.
Press the broken KitKat pieces gently onto the sides and top of the cake to decorate.
Refrigerate the cake for at least 30 minutes before serving to allow the frosting to set.