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1
Preheat the oven to 425 degrees F (220 degrees C). Line 2 jelly roll pans with parchment paper.
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2
Beat egg whites in a glass, metal, or ceramic bowl until soft peaks form. Slowly add white sugar and whip on high speed until the whites are stiff and glossy.
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3
Beat almond flour, confectioners' sugar, eggs, and egg yolks in a separate bowl for 3 minutes. Add flour and beat on low speed until combined. Gently fold egg whites into the almond mixture until combined. Divide batter between the jelly roll pans; spread evenly.
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4
Bake cake layers in the preheated oven until lightly browned, about 5 minutes. Invert onto cooling racks and peel off parchment paper; let cool.
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5
Make coffee syrup while cake is cooling. Combine boiling water, sugar, and coffee powder in a small bowl; stir until dissolved.
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6
Stir 2 tablespoons boiling water and coffee powder together for the buttercream. Set aside.
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7
Combine sugar, 1/4 cup water, and vanilla extract in a small saucepan. Bring to a boil. Cook, without stirring, until an instant-read thermometer inserted into the mixture reaches 255 degrees F (124 degrees C).
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8
Meanwhile, beat egg and egg yolk in a stand mixer on high speed until pale and foamy. Pour hot sugar syrup carefully down the side of the mixer bowl, mixing continuously until the bottom of the bowl feels cool to the touch.
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9
Beat butter in a separate bowl until creamy. Add butter gradually to the egg mixture, beating until frosting is fluffy. Add the dissolved coffee mixture and beat until well incorporated.
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10
Place dark chocolate in a heat-proof bowl. Bring milk and cream to a boil in a saucepan. Pour over chocolate; stir until melted and smooth. Whisk in butter until ganache looks smooth and creamy. Let cool.
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11
Cut cooled cake layers in half crosswise. Place 1 piece on a rectangular serving plate. Sprinkle some coffee syrup on top. Add an even layer of buttercream. Repeat with a second cake layer, more coffee syrup, and another layer of buttercream. Spread 1/2 of the ganache on top. Repeat with remaining, cake layers, coffee syrup, and buttercream. Top cake with remaining ganache.
