Cover a 5-by-12-inch piece of cardboard with foil and set aside. Lay a sheet of plastic wrap on a large baking sheet, letting the short ends overhang. Using a serrated knife, cut the angel food cake into 16 even slices and arrange on the plastic wrap, piecing the slices together to make a 12-inch square.
Working quickly, spread the ice cream onto the square in an even layer. Starting with one long side, roll up the cake jelly-roll style; cover with the plastic wrap and twist the ends of the wrap. Freeze the log until firm, about 3 hours.
In a small microwaveable bowl, microwave half of the chocolate at medium power for 1-1/2 minutes, stir, microwave again, then stir. Add the remaining chocolate, let stand briefly, then stir until smooth. Line a baking sheet with wax paper. Dip the flat side of each meringue into the chocolate just to coat. Place a mini marshmallow in the center of the meringue for a stem; transfer to the baking sheet, marshmallow side up. Let the meringue mushrooms stand until set, about 20 minutes.
Using an electric mixer or whisk, beat the egg whites and sugar over a saucepan of simmering water until the sugar melts, about 3 minutes. Remove from the heat. Beat the egg whites at high speed until stiff, then reduce the speed and beat until cool, about 5 minutes. In a medium bowl, whip the heavy cream until stiff but not dry. Gently fold the cream into the egg whites.
Unwrap the frozen cake log, place on the prepared cardboard and return to the baking sheet. Spread the whipped topping on the log (leaving the ends uncovered) in an irregular fashion, like tree bark. Sprinkle and pat the coconut all over. Trim the ends of the cake, cover each end with wax paper and freeze until ready to serve. Transfer the cake on its board to a serving platter and remove the wax paper from the ends. Decorate the platter with the meringue mushrooms.