1.To make meringue mushrooms, hold pastry tip perpendicular to a parchment paper-lined baking sheet and pipe meringue into the shapes of mushroom caps and stems of various sizes, then set aside for 5 minutes. Lightly moisten a fingertip in cold water and smooth out any "tails" left behind on mushroom caps. Bake meringues for 1 1/2 hours.
2.Bore a small, shallow hole in center of underside of each mushroom cap with the tip of a paring knife. "Glue" stems to caps by dipping tips of stems into icing, then sticking into holes in caps. Sift a little cocoa powder on tops of caps. Meringues can be stored in an airtight container at room temperature for several days.
3.Transfer roulade with parchment to a clean work surface, sprinkle with rum, then spread filling evenly over top using a metal spatula.
4.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 buche; then, to make the stumps thinner than the buche, partially unroll each piece, trim off flap, and discard. Set stumps aside.
5.Using two long metal spatulas, carefully transfer buche to a serving platter lined with strips of waxed paper. "Glue" stumps onto buche with some of the icing.
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6.Spread remaining icing on buche, dragging spatula along icing to simulate tree bark. Remove waxed-paper strips.
7.Remove waxed-paper strips. Decorate with mushrooms, then sift confectioners' sugar over mushrooms and buche.
