Preheat the oven to 350 degrees. Butter three 8-inch round cake pans, dust with cocoa, then line each pan with parchment paper.
To make the cake, in the bowl of an electric mixer fitted with the paddle attachment, combine the flour, sugar, cocoa, baking powder, baking soda, salt, and espresso powder, and mix on low speed until well combined.
Add the milk, vegetable oil, eggs, and vanilla to the flour mixture, and mix on medium speed until well combined. Reduce the speed, and carefully add the boiling water to the cake batter. Beat on high speed for about 1 minute to add air to the batter.
Distribute the cake batter evenly among the three prepared cake pans. Bake for 25 to 30 minutes until a toothpick or cake tester inserted in the center comes out clean.
Remove the pans from the oven and allow the cakes to cool for about 10 minutes. Then remove the cakes from the pans, and cool completely before icing (see recipe for icing below!)
To assemble the cake, use a serrated knife to level the tops of the cake layers, and place the first layer on a serving platter. Using an offset spatula, spread the top of that layer with ½ inch of icing. Top with the trimmed layer, and repeat icing until all three layers are stacked.
Top the cake with raspberries and a dusting of powdered sugar.