Special equipment: 10 by 15-inch jelly-roll pan, buttered and lined with buttered parchment
To make the buttercream: Whisk the egg whites and sugar together in the bowl of an electric mixer. Set the bowl over simmering water and whisk gently until the sugar is dissolved and the egg whites are hot. Attach the bowl to the mixer and whip with the whisk on medium speed until cooled. Switch to the paddle and beat in the softened butter and continue beating until the buttercream is smooth. Dissolve the instant coffee in the liquor and beat into the buttercream.
Turn the genoise layer over and peel away the paper. Invert onto a fresh piece of paper. Spread the layer with half the buttercream. Use the paper to help you roll the cake into a tight cylinder Transfer to baking sheet and refrigerate for at least 30 minutes or until set. Reserve the remaining buttercream for the outside of the buche.
To make the marzipan: Combine the almond paste and 1 cup of the sugar in the bowl of the electric mixer and beat with the paddle attachment on low speed until the sugar is almost absorbed. Add the remaining 1 cup sugar and mix until the mixture resembles fine crumbs. Add half the corn syrup, then continue mixing until a bit of the marzipan holds together when squeezed, adding additional corn syrup a little at a time, as necessary; the marzipan in the bowl will still appear crumbly. Transfer the marzipan to a work surface and knead until smooth.
To make marzipan mushrooms: Roll 1/3 of the marzipan into a 6-inch long cylinder and cut into 1-inch lengths. Roll half the lengths into balls. Press the remaining cylindrical lengths (stems) into the balls (caps) to make mushrooms. Smudge with cocoa powder. To make holly leaves: Knead green color into 1/2 the remaining marzipan and roll it into a long cylinder. Flatten with the back of a spoon, then loosen it from the surface with a spatula. Cut into diamonds to make leaves, or use a cutter.
To make holly berries: Knead red color into a tiny piece of marzipan. Roll into tiny balls.
To make pine cones, knead cocoa powder into the remaining marzipan. Divide in half and form into 2 cone shapes. Slash the sides of cones with the points of a pair of scissors.
Unwrap the cake. Trim the ends on the diagonal, starting the cuts about 2 inches away from each end. Position the larger cut piece on the buche about 2/3 across the top. Cover the buche with the reserved buttercream, making sure to curve around the protruding stump. Streak the buttercream with a fork or decorating comb to resemble bark. Transfer the buche to a platter and decorate with the marzipan. Sprinkle the platter and buche sparingly with confectioners' sugar "snow."
Storage: Keep at cool room temperature. Cover leftovers loosely and keep at room temperature.
Set rack in the middle of the oven and preheat to 400 degrees.
Half-fill a medium saucepan with water and bring it to a boil over high heat. Lower the heat so the water is simmering.
Whisk the eggs, yolks, salt, and sugar together in the bowl of a heavy-duty mixer. Place over the pan of simmering water and whisk gently until the mixture is just lukewarm, about 100 degrees (test with your finger). Attach the bowl to the mixer and with the whisk attachment, whip on medium-high speed until the egg mixture is cooled (touch the outside of the bowl to tell) and tripled in volume.
While the eggs are whipping, stir together the flour, cornstarch, and cocoa.
Sift 1/3 of the flour mixture over the beaten eggs. Use a rubber spatula to fold in the flour mixture, making sure to scrape all the way to the bottom of the bowl on every pass through the batter to prevent the flour mixture from accumulating there and making lumps. Repeat with another 1/3 of the flour mixture and finally with the remainder.
Scrape the batter into the prepared pan and smooth the top. Bake the genoise for about 10 to 12 minutes, or until well risen, deep and firm to the touch. (Make sure the cake doesn't overbake and become too dry, or it will be hard to roll.)
Use a small paring knife to loosen the cake from the sides of the pan. Invert the cake onto a rack and let the cake cool right side up on the paper. Remove the paper when the cake is cool.
Storage: Wrap in plastic wrap and refrigerate for several days, or double-wrap and freeze for up to a month.
Recipe courtesy of Nick Malgieri, "Perfect Cakes", HarperCollins, 2002