Preheat the oven to 350 degrees F (175 degrees C). Grease a 10×15-inch rimmed baking sheet and line the bottom of the pan with parchment paper.
Whisk flour, cocoa powder, baking soda, and salt together in a bowl until thoroughly combined. Set aside.
Beat brown sugar, white sugar, and butter together in a large bowl with an electric mixer until light and fluffy. Beat in eggs one at a time, mixing well after each addition. Mix in vanilla extract. Add in 1/3 of the flour mixture, and mix until just combined. Add in 1/2 of the coffee and buttermilk, and mix until just combined. Continue alternating additions of the flour mixture with coffee and buttermilk, mixing just until combined. Pour batter into the prepared pan; smooth into an even layer. Tap pan firmly on the counter several times to remove air bubbles.
Bake in the preheated oven until a toothpick inserted into the center of the cake comes out with a few moist crumbs, about 25 minutes. Do not overbake. Place cake on a wire rack and allow to cool completely.
Meanwhile, make the frosting. Beat butter in a large bowl until completely smooth. Mix in cocoa powder, espresso powder, and salt until thoroughly combined. Mix in vanilla. Add in powdered sugar 1 cup at a time, mixing well after each addition. Pour in heavy cream and beat until frosting is light and fluffy, 2 to 3 minutes. If frosting is too thick, add more heavy cream.
Spread frosting over the cooled cake.
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