Preheat your oven to 350°F (175°C). Grease and flour two 9-inch round cake pans.
In a large mixing bowl, combine the flour, sugar, cocoa powder, baking powder, baking soda, and salt. Whisk together until well blended.
Add the eggs, milk, vegetable oil, and vanilla extract to the dry ingredients. Beat on medium speed for 2 minutes until smooth.
Carefully stir in the boiling water until the batter is well combined (the batter will be thin).
Pour the batter evenly into the prepared cake pans. Bake for 30-35 minutes or until a toothpick inserted in the center comes out clean.
Allow the cakes to cool in the pans for 10 minutes, then remove them from the pans and transfer to wire racks to cool completely.
For the frosting, beat the softened butter in a medium bowl until creamy. Gradually add the cocoa powder and powdered sugar, alternating with the milk, and mix until smooth. Stir in the vanilla extract.
Once the cakes are completely cool, place one layer on a serving plate and spread a layer of frosting on top. Place the second layer on top and frost the top and sides of the cake.
Serve immediately or refrigerate for up to 3 days.