1 cup (2 sticks) unsalted butter, room temperature
1/2 cup confectioner's sugar
Generous pinch of coarse salt
1 pound semisweet chocolate, melted and cooled
Make the cake: Preheat oven to 350 degrees. Butter two 8-by-2-inch round cake pans, line bottoms with parchment paper, and butter paper. Whisk together cocoa powder and hot water until smooth.
Sift together flour, salt, baking powder, and baking soda; set aside. Melt butter and sugar in a saucepan over medium-low heat. Remove from heat, and transfer to a mixer. Beat on medium-low speed until cooled, 4 to 5 minutes.
Add eggs, one at a time, beating after each addition. Beat in vanilla and cocoa-powder mixture. Reduce speed to low. Add flour mixture in two batches, alternating with sour cream and beginning and ending with flour. Beat until just combined.
Divide batter between pans, and bake until a cake tester inserted into centers comes out clean, 45 to 50 minutes. Transfer pans to a wire rack to cool for 15 minutes. Invert cakes onto rack, peel off parchment, and let cool completely.
Make the frosting: Whisk together cocoa powder and hot water until smooth. Beat butter, sugar, and salt in a mixer on medium-high speed until pale and fluffy. Reduce to medium-low speed; slowly add melted chocolate and cocoa-powder mixture, and beat until combined. If frosting is not set, let stand, stirring occasionally until thickened, 20 to 30 minutes.
Using a serrated knife, trim tops of cake layers to make level. Transfer one cake layer to a cake stand, and spread with 1 cup frosting. Top with remaining cake layer, and coat top and sides with remaining frosting, spreading it in a swirling motion.
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