Whip together 1 1/2 cups of the heavy cream, the confectioners' sugar and espresso powder in a large bowl with an electric mixer on medium-high speed until stiff peaks form, 2 to 3 minutes.
Spread a heaping tablespoon of the whipped cream onto one side of 39 chocolate wafer cookies (wipe the spoon clean with a rubber spatula between dollops). Spread the whipped cream out on the cookies with a small offset spatula. Stack 5 cookies on top of each other. Repeat with the remaining cookies (including the one without whipped cream) so that you have 8 stacks total. One of the stacks will have a cookie on top with no whipped cream; this stack will be the top stack.
To build the log: Lay out a piece of plastic wrap about 20 inches long on the countertop. Working across the entire length of the plastic wrap, lay one of the cookie stacks on its side. Gently press the remaining 7 cookies stacks together, end to end, finishing with the top stack, to make one long cookie log that's about 15 to 18 inches long. Wrap the log up in the plastic wrap and chill for at least 4 hours and up to overnight.
While your stack is chilling, make the ganache: Put the chocolate in a medium bowl. Bring the remaining 1 1/2 cups heavy cream to a boil in a small saucepan and pour over the chocolate. Let sit for 10 minutes, then stir until completely melt. Pour the mixture into the bowl of an electric mixer and refrigerate until completely cool, about 30 minutes. Just before frosting, whip the ganache until it just begins to loosen up, turns lighter in color and is spreadable, 30 to 45 seconds. It's important not to overwhip or it will become grainy.
Cut a 2- to 3- inch diagonal piece from the top end of the log and place it on top of the log at an angle; this will be the branch. Spread the ganache over the log to cover it completely. Heat a metal fork. Use the tines and the back of a the fork to draw a bark pattern in the ganache, running it along the surface in short strokes.
To make the mushrooms: Shave the tops of 6 of the meringues with a rasp grater until they are smooth and round and resemble mushroom caps. Smooth the tops with a wet finger. Mix together 2 tablespoons confectioners' sugar with 1/4 teaspoon water in a small bowl to make a glue. Smear a little of the sugar glue on the bottom of each meringue and stick a marshmallow to it to make a stem. To make a shorter stem, simply cut the marshmallow in half with kitchen shears. Let the mushrooms sit for 30 minutes until the sugar water has hardened. Dust the tops with cocoa powder.
Decorate the cake with the mushrooms, rosemary, mint and cranberries. Shave the remaining meringue over top of the cake to make snow. Slice the cake on a diagonal for serving.
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