Make cake layers:
- Put oven rack in middle position and preheat oven to 350°F.
- Butter 2 (9- by 2-inch) round cake pans and line bottom of each with a round of wax paper.
- Butter paper and dust pans with flour, knocking out excess.
- Whisk together hot water and cocoa powder in a bowl until smooth, then whisk in milk and vanilla.
- Whisk together flour, baking soda, and salt in another bowl.
- Beat together butter and brown sugar in a large bowl with an electric mixer at medium-high speed until pale and fluffy, 3 to 5 minutes.
- Add eggs 1 at a time, beating well after each addition.
- Reduce speed to low and add flour and cocoa mixtures alternately in batches, beginning and ending with flour mixture (batter may look curdled)
- Divide batter between cake pans, smoothing tops.
- Bake until a wooden pick or skewer comes out clean and edges of cake begin to pull away from sides of pans, 25 to 35 minutes total.
- Cool layers in pans on racks 10 minutes, then invert onto racks, removing wax paper, and cool completely.
- Assemble cake: Put 1 cake layer, rounded side up, on a cake stand or platter and, using offset spatula, spread top with about 1 cup buttercream. Top with remaining cake layer, rounded side down, and frost side and top of cake with 2 cups buttercream.
- Decorate cake: For each colour (you can make up to 5), transfer 3 tablespoons buttercream to a separate small bowl and tint with food coloring.
- Snip off 1 corner of each plastic bag to create a 1/4-inch opening, then spoon each color of buttercream into a bag, pressing out excess air.
- Twist each bag firmly just above buttercream, then decoratively pipe colored buttercream onto cake.
- Chill cake until buttercream is set, about 30 minutes.
- Just before serving, arrange 6 to 8 mini cupcakes on top of cake in 1 layer, then stack remaining mini cupcakes on top.