Būche de Noėl
5. To assemble the būche: Transfer roulade with parchment to a clean work surface, sprinkle with rum, then spread filling evenly over top using a metal spatula. Grab the long edge of the parchment paper with two hands and gently roll roulade onto itself, pulling off paper as you roll. To make stumps, diagonally cut a 2" length from each end of būche; then, to make the stumps thinner than the būche, partially unroll each piece, trim off flap, and discard. Set stumps aside.
6. Using two long metal spatulas, carefully transfer būche to a serving platter lined with strips of waxed paper. "Glue" stumps onto būche with some of the icing. Melt 1/4 cup of icing in a saucepan over low heat, then spoon it over stumps to coat completely. Spread remaining icing on būche, dragging spatula along icing to simulate tree bark. Remove waxed-paper strips. Decorate with mushrooms, then sift confectioners' sugar over mushrooms and būche.