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1
For the filling: Bring the cream to a -simmer in a small saucepan over high heat. Off the heat, stir in the confectioners' sugar and espresso and let cool slightly. Gently whisk the cooled cream mixture into the softened mascarpone until combined. Cover with plastic wrap and refrigerate until ready to use.
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2
For the frosting: Place the chocolate in a food processor. Bring the cream, corn syrup and salt to a boil in a liquid measuring cup in the microwave. Stir the mixture to combine.
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3
Pour the hot cream mixture over the chocolate in the food processor and process until the mixture is smooth, about 1 minute.
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4
Add the sugar and vanilla nad continue to process until combined, about 30 seconds. With the machine running, add the softened butter, one piece at at time, through the feed tube. Continue to process until the frosting is smooth and no butter chunks remain, about 2 minutes.
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5
Transfer the frosting to a small bowl, cover with plastic wrap and refrigerate until thick and spreadable, about 1 hour.
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6
For the cake: Adjust an oven rack to the lower-middle position and heat the oven to 350 degrees. Grease an 18 by 13-inch rimmed baking sheet, line the bottom with parchment paper, and grease the paper. Whisk the flour, cocoa, baking powder, and salt together in a medium bowl.
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7
In a large bowl, whip the eggs with an -electric mixer on medium-high speed and gradually add the sugar, about 1 minute. Continue to whip the mixture until very thick and voluminous, 4 to 8 minutes. Whip in the vanilla. Sift the flour mixture over the egg mixture and fold with a rubber spatula until just incorporated.
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8
Scrape the batter into the prepared baking sheet and spread out to an even layer. Bake the cake until it feels firm and springs back when touched, 12 to 17 minutes, rotating the pan halfway through baking.
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9
Immediately run a knife around the edge of the cake and flip the hot cake out onto a large sheet of greased parchment paper. Peel off and discard the parchment paper baked on the -bottom of the cake. Starting from a long end, roll the cake snugly around the large sheet of -parchment into a log and let cool for 15 minutes.
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10
Beat the filling until stiff with an electric mixer on medium-high speed, 10 to 30 seconds. Gently unroll the cake. Spread the filling over the cake, leaving a 1/2-inch border at the edges. Reroll the cake gently but snugly around the filling. Following the photos, cut a 2- to 3-inch piece off one end of the cake at an angle and reserve.
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11
Line the edges of a cake platter with strips of parchment and arrange the chocolate roll on the platter. Frost the cake evenly with 2 cups of the frosting. Attach the reserved trim piece on top of the cake (to look like a stump) and frost with the remaining frosting. Using a fork, make a wood grain pattern in the frosting all over the cake.
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12
To decorate: If desired, lightly dust the entire cake with confectioners' sugar to look like snow. Remove the parchment strips before serving.
