Preheat your oven to 350°F (175°C). Grease and flour two 9-inch round cake pans.
In a large bowl, stir together the flour, sugar, cocoa, baking powder, baking soda, and salt.
Add the eggs, milk, oil, and vanilla. Beat on medium speed for 2 minutes. Stir in the boiling water (batter will be thin).
Pour the batter into the prepared pans.
Bake for 30 to 35 minutes, or until a toothpick inserted into the center comes out clean. Cool in the pans for 10 minutes, then remove to wire racks to cool completely.
For the frosting, beat the butter until creamy. Gradually add the powdered sugar and cocoa powder, beating until smooth. Add the heavy cream and vanilla, and beat until fluffy.
Frost the cooled cakes.