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, cocoa powder, sugar, 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 cakes from the oven and allow them to cool in the pans for 10 minutes.
Turn the cakes out onto wire racks to cool completely.
To make the vanilla frosting, beat the softened butter on medium speed until creamy, about 2 minutes.
Gradually add the powdered sugar, one cup at a time, beating on low speed until incorporated.
Add the milk, vanilla extract, and salt. Beat on high speed for 3 minutes until light and fluffy.
Once the cakes are completely cool, place one cake layer on a serving plate.
Spread a thick layer of vanilla frosting over the top.
Place the second cake layer on top and frost the top and sides of the entire cake.
Smooth the frosting with a spatula or create decorative swirls as desired.
Refrigerate the cake for 30 minutes before serving to set the frosting.