Adapted from Bon Appetit
1/2 cup unsweetened cocoa powder
1 cup lukewarm water, divided
1/2 cup buttermilk
1 1/2 cups cake flour
3/4 teaspoon baking soda
1 cup sugar
1/2 cup packed brown sugar
1 stick (8 tablespoons) butter, at room temperature
2 large eggs, at room temperature
1 1/4 sticks butter (10 tablespoons)
1 1/3 cups packed brown sugar
1 cup unsweetened cocoa powder
1 teaspoon instant espresso powder
1 cup heavy cream
2 teaspoons vanilla
Preheat oven to 350º. Butter 3 9-inch cake pans. Line bottoms with parchment and butter top of parchment. Set aside.
Whisk the cocoa and 1/2 cup of the warm water in small bowl or liquid measuring cup to combine. Whisk buttermilk with other 1/2 cup of warm water in small bowl or liquid measuring cup to combine. Sift the flour and baking soda into another bowl.
With mixer, beat butter and two sugars in a large bowl till pale yellow and fluffy, about 5 minutes. With mixer running, add eggs and beat till combined, scraping edges of bowl as needed. Add cocoa mixture and blend. Add flour mixture in 3 additions, alternating with 2 additions of buttermilk. Beati till just combined, stopping to scrape down bowl as necessary. Divide batter evenly between the 3 pans...about 1 1/2 cups per pan.
Bake for 16 to 18 minutes or till cake pops back when pressed lightly with finger in the center of cake...rotate pans half way through baking time to ensure even baking. Cool completely on racks.
Make frosting by melting butter in large saucepan over medium-low heat. Stir in brown sugar, cocoa, and espresso powder. Gradually stir in cream, and continue stirring till mixture is hot. When cream is just about to boil, reduce heat to low and cook another minute. Remove from heat and stir in vanilla. Pour into bowl and chill for about 1 1 /2 hours to thicken, stirring occasionally.
To assemble cake, run knife around sides of cake. Gently shake back and forth till cake loosens from bottom. Carefully flip one layer onto serving plate...cake is fragile. Remove parchment. Spread about 1/2 cup frosting on top of cake and spread to edges. Repeat with second layer. Top with third layer and use the rest of the frosting to ice top and sides of cake.