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Preheat oven to 350 degrees. Butter two 9-by-2-inch round cake pans; line bottoms with parchment paper. Butter parchment; dust with cocoa powder, tapping out excess.
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In a medium bowl, whisk cocoa with hot water until smooth. Whisk in sour cream; let cool. Into a medium bowl, sift together flour, baking soda, and salt; set aside.
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In the bowl of an electric mixer fitted with the paddle attachment, beat butter and sugar on medium speed until light and fluffy, 3 to 4 minutes. Add eggs, one at a time, beating to combine after each; scrape down sides of bowl as needed. Beat in vanilla. With mixer on low speed, add flour mixture in two parts, alternating with the cocoa mixture and beginning and ending with the flour; beat until combined.
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Divide batter between prepared pans (or cupcake tins); smooth with an offset spatula. Bake until a cake tester inserted in center comes out clean, 45 to 50 minutes (or 18 to 20 minutes for cupcakes).
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Transfer pans to a wire rack to cool 15 minutes. Invert cakes onto rack; peel off parchment. Re-invert cakes; let cool completely, top sides up.
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Make the frosting: Finely chop both the bittersweet and milk chocolates. Place into a mixing bowl. Set aside.
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In a small saucepan, bring heavy cream and corn syrup to a boil. Take off the heat and pour over chocolate. Let stand for 2 to 3 minutes.
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Starting in the center, whisk towards the edges of the bowl until the chocolate is smooth. Let cool at room temperature.
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Using a stand mixer with a whisk attachment, beat at medium speed and gradually add butter until frosting is smooth and silky.
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Using a serrated knife, trim tops of cake layers to make level. Transfer one of the layers to a cake turntable or platter to frost. With an offset spatula, spread top with 3/4 cup milk chocolate frosting. Place the second cake layer on top.
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For the crumb coat, spread the entire cake with a thin coat of frosting using an offset spatula. Chill for at least 30 minutes.
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Spread the entire cake with remaining frosting, swirling to coat in a decorative fashion. Serve immediately, or refrigerate, covered with a cake dome. Let sit at room temperature for about 20 minutes before serving.
