Instructions

1. Make the chocolate ganache: Place a large fine-mesh strainer over a deep glass bowl. In a food processor, process the chocolate until very fine.
2. In a small pot over medium heat, bring the cream just to a boil. With the processor running, pour the cream through the feed tube in a steady stream. Process for a few seconds until smooth, scraping down the sides of the processor as needed. Press the ganache through the strainer and scrape any mixture clinging to the underside into the bowl. Set aside at room temperature for 1 hour.
3. Cover the ganache with plastic wrap or a lid and set aside until it reaches a soft frosting consistency (75°F–80°F), 2–3 hours. (The ganache can be stored in an airtight container at cool room temperature for 3 days, in the fridge for 2 weeks, or in the freezer for 3 months.)
4. Make the meringue mushrooms (if desired): Position racks in the upper and lower thirds of the oven and preheat to 200°F.
5. Beat the egg whites to a stiff meringue: In a stand mixer fitted with the whisk attachment, beat the cream of tartar and egg whites on medium-low until foamy. Gradually turn the speed to medium-high and beat until soft peaks form when the whisk is raised, about 4 minutes. Beat in 1 tablespoon of the sugar and continue beating until stiff peaks form when the whisk is raised slowly, about 1½ minutes more. Scrape down the sides of the bowl. Gradually add the remaining ½ cup of sugar. Beat on high until the meringue is very stiff and glossy, about 5 minutes. Detach the whisk and bowl from the stand. Tap the whisk against the sides of the bowl as needed to release the meringue from the center. 
6. Line two large baking sheets with a silicone baking mat, parchment, or foil. Fit a piping bag with a number 3 round decorating tip and a second bag with a number 6 large round tube (½ inch in diameter). Fill the bags with the meringue mixture, placing about ¼ cup in the bag with the small tip and the rest in the bag with the large tip. Clean and dry the bowl and whisk attachment.
7. Pipe the mushroom caps: Hold the bag with the larger tip upright with the tip slightly above the baking sheet. Squeeze with a steady, even pressure, gradually raising the tip as the meringue begins to build up but keeping the tip buried in the meringue. When you have achieved a well-rounded shape, stop the pressure as you bring the tip to the surface. Use the edge of the tip to shave off any point by rotating the bag clockwise, or smooth the points down by pressing gently with a moistened fingertip. Continue piping a total of 30 caps.
8. Pipe the mushroom stems: Hold the bag with the larger tip perpendicular to the baking sheet with the tip touching it. Squeeze with heavy pressure, lifting the bag but keeping the tip buried in the meringue until you build a ¾-inch-high cone. Continue piping a total of 30 stems.
9. Bake until the meringues are pale golden, crisp, and firm enough to lift from the baking sheet, about 45 minutes. 
10. Assemble the mushrooms: With the tip of a paring knife, make a small hole in the underside of each cap. Using the piping bag with the smaller tip, pipe a tiny dab of meringue into the hole and attach a stem by inserting the pointed end. Place the mushrooms, caps down, on the baking sheet and continue baking until thoroughly dry, about 20 minutes more. To test for doneness, dig a small amount of the meringue from the center, or for smaller shapes, break one of them with the tip of a small knife. The interiors should be only slightly sticky. (If only slightly, it will continue to dry at room temperature.) If necessary, continue baking for about 10 minutes more. Place the sheet on a wire rack and use a thin offset spatula to transfer the meringues to another wire rack to cool completely. If not assembling the cake immediately, store the cooled meringues in an airtight container at room temperature. 
11. Make the whipped cream: In a medium metal bowl, whisk together the cream, sugar, and vanilla just until the sugar dissolves. Cover and refrigerate, along with the beaters of a hand mixer, for at least 15 minutes or up to 24 hours. (If refrigerating for longer than an hour, cover the bowl with plastic wrap.)
12. Make the cake: Position a rack in the center of the oven and preheat to 350°F. Lightly grease an 18- by 13-inch rimmed baking sheet with nonstick spray, then line with a piece of parchment cut to extend 1 inch past each of the long sides of the sheet. Coat the parchment with nonstick spray and set aside.
13. In a small microwave-safe bowl, microwave the chocolate in 15–30-second increments, stirring with a silicone spatula between each increment, until almost completely melted, about 2 minutes. (Alternatively, melt the chocolate in the top of a double boiler set over hot, not simmering, water—do not let the bottom of the container touch the water—stirring frequently with a silicone spatula. Remove the chocolate from the heat and stir until fully melted.) Set the chocolate aside to cool until no longer warm to the touch but still fluid, about 15 minutes.
14. To the stand mixer fitted with the whisk attachment, add the egg yolks and ¼ cup of the sugar and beat on low until homogeneous. Turn the mixer to high and beat until the mixture is thick, fluffy, tripled in volume, and falls in ribbons when the whisk is raised, about 5 minutes. Scrape in the melted chocolate and beat on medium, using a silicone spatula to scrape down the sides and bottom of the bowl as needed, until evenly incorporated. If you do not have a second stand mixer bowl, scrape this mixture into a large bowl and thoroughly wash, rinse, and dry the mixer bowl and whisk attachment to remove any traces of fat.
15. To the bowl of the stand mixer fitted with the whisk attachment, add the egg whites and cream of tartar and beat on medium-low until foamy, about 1½ minutes. Gradually turn the mixer to medium-high and beat until the meringue forms soft peaks when the whisk is raised, about 1½ minutes more. Gradually beat in the remaining 2 tablespoons of sugar and continue beating until the meringue forms stiff peaks when the whisk is raised slowly, about 5 minutes.
16. Using a silicone spatula, scrape about one-quarter of the meringue into the yolk-sugar-chocolate mixture, then stir and fold together until incorporated. Gently fold in the remaining meringue in two parts, taking care to reach to the bottom of the bowl to ensure that the meringue is fully incorporated. Pour the batter into the prepared baking sheet and smooth the surface evenly with an offset spatula. Bake until the cake has puffed, lost its shine, and springs back when pressed lightly in the center, 16–18 minutes. Meanwhile, moisten a thin, lightweight kitchen towel and wring it out well. 
17. Transfer the baking sheet to a wire rack and, while the cake is still hot, using a fine-mesh strainer, sift the cocoa evenly over the surface. Cover immediately with the damp towel and set aside to cool to room temperature. (This step is essential to prevent cracking when it comes time to roll the cake.)
18. Meanwhile, using a hand mixer, whip the chilled cream mixture, starting on low and gradually turning the mixer to medium-high as it thickens. Continue beating until the cream mounds softly when dropped from a spoon or just until stiff peaks form when the beaters are raised, about 3 minutes. (The whipped cream can be stored in an airtight container in the fridge for up to 3 hours; whisk lightly before using.)
19. Remove the towel and use the long edges of the parchment to gently transfer the cake from the baking sheet to a large cutting board. Spread immediately with the whipped cream and, still using the parchment for support and gently peeling it away as you go, roll the cake up from the long side to make a tight and even log shape. Refrigerate until firm and chilled, at least 1 hour or up to 24. (If refrigerating for longer than an hour, cover with plastic wrap.)
20. Cut a 1–1½-inch diagonal slice from one end of the roll and place it on top to suggest a knot in the wood. Spread the chocolate ganache over the log and use the tines of a fork to make lines resembling bark. Make a few round swirls with the fork on top of the knot to simulate rings. Decorate with the meringue mushrooms and refrigerate for at least 1 hour. 
21. Using a large, thin knife, cut into slices and serve slightly chilled or at room temperature.