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Preheat oven to 400 degrees.
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Lightly grease a 12-by-15-inch sheetcake or jelly-roll pan and line it with aluminum foil or baking parchment, leaving an overhang of about an inch on each end.
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Grease and lightly flour the foil or paper.
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Toast hazelnuts in oven until they turn dark brown, about 7 minutes.
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If nuts are unblanched rub in a towel to remove skin.
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Let nuts cool; then grind until fine in a processor with 1/4 cup sugar.
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In bowl of an electric mixer, beat 6 egg yolks with remaining 1/3 cup sugar until pale and stiff, about 5 minutes.
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In a clean, dry copper bowl or the bowl of an electric mixer - or using a hand-held electric beater -whip 7 egg whites slowly until they start to foam.
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Increase speed to medium.
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When they are opaque white, add salt and beat at medium speed until stiff white peaks form, about 3 minutes.
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Alternately fold the sifted flour, nuts and half the whites into yolks.
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The batter will be thick.
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When all components are incorporated, fold in remaining whites.
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Remove 1 cup of the mixture and stir the melted butter into it.
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Fold into the batter.
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Spread batter on prepared sheetcake or jelly-roll pan with a spatula, spreading evenly to corners and along sides; try not to deflate batter.
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Bake 5 to 6 minutes, until cake just springs back when pressed.
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It is better to underbake it slightly.
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Remove cake from pan using the overhanging piece of foil or paper.
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Set on a counter or rack.
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Turn over onto another baking sheet and carefully peel off foil or paper.
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Turn over again onto a clean sheet of foil, and cover with towel.
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With an electric mixer whip the yolks at medium speed until pale, thick and creamy, about 5 minutes.
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24
In a small saucepan, stir together sugar and water.
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Boil until you can form a soft ball with a bit of syrup dropped from a spoon into a bowl of cold water; it should register 242 degrees on a candy thermometer.
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This takes 3 to 4 minutes after the syrup comes to a boil.
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With mixer running, slowly pour the syrup in a thin stream into the center of the yolks.
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Beat at slow to medium speed until mixture is cool, about 10 minutes.
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With mixer still running, slowly add the softened butter to the yolks and beat at low speed until completely smooth, about 5 minutes.
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If even after 5 minutes the cream still has small lumps, remove about a half-cup to a bowl and beat it over hot water until it is smooth; return to the mixer bowl and all of the cream should become smooth, with the consistency of creamed butter.
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(You can repeat this process several times.)
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Increase speed to medium and continue beating 10 minutes, until butter cream billows like whipped cream and shows large air holes when a spoon is run through it.
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Beat in dissolved coffee.
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To assemble buche, use a spatula to spread butter cream over the cake.
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The cream layer should be less than 1/4 inch thick.
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Crumble all but 3 marrons glaces over the butter cream.
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Using the foil as a support, roll up the cake by the long end to form a log shape.
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Trim ends.
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To decorate, place a ruler over length of the log and sift confectioners' sugar over log.
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Remove ruler and arrange slices of reserved marrons glaces down the length.
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Transfer to a serving platter.
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Buche is best left at room temperature and served within 3 to 4 hours, but it can be refrigerated for a day.