Preheat oven to 350°F (175°C). Grease and flour two 9-inch round cake pans.
In a large bowl, whisk together flour, sugar, cocoa powder, baking powder, baking soda, and salt.
Add milk, vegetable oil, eggs, and vanilla. Beat on medium speed for 2 minutes until smooth.
Stir in boiling water (batter will be thin). Pour into prepared pans.
Bake for 30–35 minutes or until a toothpick inserted in center comes out clean. Cool 10 minutes, then remove from pans and cool completely on wire racks.
For frosting: In a saucepan, heat milk and butter over low heat until steaming. Remove from heat and stir in cocoa powder until smooth.
Gradually beat in powdered sugar, then vanilla. Spread between cooled layers and over top of cake.
Notes
Best served at room temperature. Store covered at room temperature for up to 3 days.