Set the rack in the middle of the oven and preheat to 400° F.
Fill the 2-quart sauce pan halfway with water. Bring to a boil and then reduce heat to a simmer.
In the bowl of the stand mixer, whisk together the eggs, egg yolks, sugar, and salt. Set the bowl over the pan of simmering water and stir gently until the mixture reaches about 100 degrees or feels just warm to the touch. Remove from heat.
Using the whisk attachment, whip on medium-high speed until the egg mixture is cool to the touch and triples in volume. The egg mixture should be thick and make a ribbon as it drips off the whisk back into the bowl.
In the small bowl, stir together the flour, cornstarch, and chocolate. Sift ⅓ of the dry ingredients over the egg mixture. Using a spatula, fold in the flour. Make sure you get all the way to the bottom of the bowl and pull up any of the flour mixture. Repeat with another third of the flour mixture, and then with the last of the flour. There should be no dry lumps or specks.
Pour the batter into the prepared pan and smooth the top so that the cake is distributed evenly throughout the pan.
Bake for 10 to 12 minutes. (Start making the filling.) The cake should spring back when touched and a tester should come out clean. Make sure it does not cook too long because it can dry out, making it difficult to roll. Remove cake from oven and allow it to sit in the pan on a wire rack.
CHOCOLATE CREAM CHEESE FILLING
In the bowl of the stand mixer (paddle attachment), mix together the softened cream cheese and the sugar at medium speed until it is creamy.
Make sure the melted chocolate has cooled. Add it to the cream cheese mixture and mix at medium speed until the chocolate color is even throughout. Scrape down the sides as necessary.
Stir in the milk and vanilla extract. Add additional milk as necessary to keep the filling from getting stiff.
ASSEMBLY PART 1
Run a knife around the edges of the pan to loosen the cake.
Turn the cake pan over onto a flat surface. Lift away the pan and remove the parchment paper.
Lay another piece of parchment nearby and dust it with powdered sugar. Carefully turn the cake over and place it on the new parchment.
Gently spread the chocolate cream cheese filling on the cake, staying about one inch away from the edges.
Carefully turn over one long edge of the cake onto itself, pressing on the parchment. Continue rolling the cake, using the parchment to keep the cake snug all the way. The cake may crack a little, and that’s ok because you will cover the cracks with the buttercream.
Make sure the cake is laying seam-side down. Wrap the parchment around the cake and then wrap in the towel. Gather the ends and tie them up as shown in the photo above. Place on a sheet pan in the refrigerator and chill for several hours or overnight.
(Prepare up to 2 days in advance and refrigerate. Return to room temperature before decorating the cake.)
In the 2-quart sauce pan, add water to about half full. Bring to a boil then reduce heat to a simmer. Dissolve the espresso powder in the vanilla.
In the bowl of the stand mixer, whisk together the egg whites and the sugar. Set the bowl over the pan of simmering water and stir gently until the sugar is fully dissolved and the egg whites are hot.
Using the whisk attachment, whip the eggs and sugar until the mixture is cool to the touch. Attach the paddle and beat in the softened butter. Continue beating until the mixture is smooth.
Add the melted and cooled chocolate and beat until the chocolate color is even throughout. Slowly add the vanilla espresso mixture 1 teaspoon at a time, mixing each time. (Add slowly to make sure the buttercream doesn’t curdle.)
(Prepare up to 3 days in advance and store in an airtight container.)
In the bowl of the stand mixer (paddle attachment), beat the marzipan and half the sugar on low speed until the sugar is absorbed. Add the remaining sugar and mix it in. It will look like fine crumbs.
Add 2 tablespoons of corn syrup and stir until the mixture starts to hold together when pressed with your hands. You may need to add a little more corn syrup, just test the consistency of the mixture as you go. It should still feel dry and crumbly, not sticky.
Knead the marzipan on a sheet of wax paper until it is smooth. If the marzipan is still crumbly, you can dip your fingers in a little corn syrup and continue kneading.
Roll the marzipan into a cylinder and cut into 1-inch lengths. Roll half of the pieces into balls and shape like mushroom caps. Take the remaining pieces and form bases of the mushrooms and press the caps and bases together.
Smudge the mushrooms with a little cocoa powder.
Remove the cake from the refrigerator and unwrap it. Using a sharp knife, cut away the two ends on a diagonal starting about 2 inches from each end.
Place pieces of wax paper on the serving plate. Lay the large piece of log on the wax paper. Place one of the cut pieces on top of the log and hold in place with two toothpicks. Push the toothpicks in deep so that they are not visible. Lay the other cut piece alongside the log.
Spread the buttercream all over the cake, including the exposed ends and the bumps. Spread the buttercream in long strokes. Use a fork to draw lines in the buttercream resembling bark.
Carefully pull away the wax paper and place the rosemary sprigs and red hots on the cake and tuck some rosemary sprigs around the plate. Place the mushrooms on the cake. Dust the cake lightly with some powdered sugar to look like snow.