5 large eggs, at room temperature
1/2 cup (99g) granulated sugar
1/2 teaspoon salt
1 tablespoon Pure Vanilla Extract
1/2 cup (60g) All-Purpose Flour
1/3 cup (28g) cocoa powder
3 tablespoons (21g) cornstarch
1 teaspoon espresso powder
1 teaspoon baking powder
1/4 cup (50g) vegetable oil
6 tablespoons (85g) buttermilk, at room temperature
For sugared rosemary and cranberries:
Simple syrup
Granulated Sugar
2 small plates
cooling rack over baking sheet
Rosemary sprigs
Cranberries
Fondant or gumpaste mushrooms (optional)
Powdered sugar
Preheat the oven to 350°F. Line a rimmed half-sheet pan (12" x 17") with parchment and grease the parchment and pan.
In a large bowl, beat the eggs until thick and pale, then beat in the sugar, salt, and vanilla. Beat until the mixture is thick and the whisk leaves tracks in the bowl. Be patient, this can take awhile.
While the eggs are beating sift together the flour, cocoa, cornstarch, espresso powder, and baking powder.
When the egg mixture is ready, add a third of the dry ingredients into the bowl and gently fold in; it’s OK if the batter is streaky at first. Repeat twice more until all the dry ingredients have been incorporated.
Whisk together the oil and buttermilk and fold into the batter, mixing just until combined.
Pour the batter into the pan and lightly smooth the top with a spatula; it will be thin and might not quite reach the corners: that’s OK. Bake the cake for 10 to 12 minutes, until the top springs back when lightly pressed.
Remove the cake from the oven and let it cool in the pan for 2 minutes.
Use the parchment under the cake to loosely roll the cake up from the long side, rolling the parchment up with it (if the serving platter you will be using is short, you can roll it from the short side instead.) Place it on a rack and let it cool completely, leaving it rolled as it cools.
Make the sugared rosemary and cranberries. Put some simple syrup in a pan and warm it. Put some sugar on a plate.
Put the rosemary sprigs in the syrup for several seconds, then move them to the cooling rack and let excess drip off. Repeat with some cranberries. After a few seconds, roll in the granulated sugar and return to the cooling rack to dry.
Make the ermine frosting.
Make the chocolate frosting.
Unroll the cooled cake, as much as it can unroll without breaking, and spread the filling inside, leaving 1” on a long end uncovered. As you roll the cake up the filling will get pushed to cover this part.
Gently roll the cake back up and place seam-side down on a large serving platter. 
Pipe frosting lines all around the outside in a layer about 1/4” thick to resemble bark.
Refrigerate long enough for the frosting to firm up.
Optional: Before frosting, use a large, sharp knife to cut one end off at an angle. Carefully move it so that the angled side is against the side of your log. Frost as needed to connect the pieces.
Add any additional layers of "bark" details to your branches if desired. Chill again until newly frosted parts firm up.
Dust the cake lightly with powdered sugar and decorate with the sprigs and cranberries, and if desired, mushrooms.(*1)
Lightly cover with plastic wrap. Leave in the fridge until ready to serve.
Slice relatively thin.
*If you are making the cake a day ahead, don’t add the powdered sugar or decorations until the next day.