Preheat the 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; this is normal.
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 from the oven and allow the cakes to cool in the pans for 10 minutes. Then remove from pans and cool completely on a wire rack.
To make the frosting, beat the softened butter on medium speed until creamy, about 2 minutes.
Gradually add the powdered sugar and cocoa powder, alternating with the milk, beating on low speed until combined.
Add the salt and vanilla extract, then 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, even layer of frosting on top.
Place the second cake layer on top and apply a thin crumb coat of frosting over the entire cake. Chill for 15 minutes.
Apply the remaining frosting evenly over the top and sides of the cake for a smooth finish.
Serve at room temperature.