Preheat your oven to 350 degrees Fahrenheit.

In a large bowl, whisk together the sugar, flour, cocoa powder, baking powder, baking soda and salt until well combined.

Add the eggs, the milk, the vegetable oil and the vanilla, and whisk these ingredients into the dry ingredients until the mixture is smooth.

Slowly add the boiling water, whisking constantly until the cake batter is runny and smooth.

Pour the cake batter into a greased 9-inch by 13-inch rectangular pan and bake at 350 degrees Fahrenheit for about 30 minutes, or until a toothpick inserted into the middle of the cake comes out clean.

Let the cake cool in the pan on a wire rack while you make the frosting.

For the frosting, whip the butter on high speed using a stand mixer or electric hand mixer until the butter is pale and smooth. Add the cocoa powder and the powdered sugar and continue to whip until everything is combined and smooth.

If necessary, add the milk a few drops at a time to loosen up the frosting until it reaches a consistency that is spreadable. This step may not be necessary depending on the temperature of the butter you used for the frosting.

When the cake has cooled completely, spread the frosting over the cake.

Refrigerate the cake for about 1 hour to allow the frosting to set before serving, or serve immediately if you desire.