Preheat the oven to 350°F (175°C)
Line a jelly roll pan with parchment paper and grease it lightly
Beat eggs and sugar until thick and pale
Add vanilla extract
Sift together flour, cocoa powder, baking powder, and salt
Fold the dry ingredients into the egg mixture
Spread the batter evenly in the prepared pan
Bake until the cake springs back when touched
Dust a clean kitchen towel with powdered sugar
Turn the warm cake onto the towel
Peel off the parchment paper
Roll the cake up in the towel from the short end
Let the cake cool completely while rolled
Make the filling by whipping heavy cream with powdered sugar and vanilla
Unroll the cooled cake carefully
Spread the filling evenly over the cake
Roll the cake back up without the towel
Place the cake seam-side down on a serving platter
Trim the ends for a neat finish
Make the frosting by beating butter, powdered sugar, cocoa powder, and milk
Spread the frosting over the outside of the cake
Create a bark-like texture with a fork or spatula
Dust with powdered sugar
Decorate with berries, rosemary, or meringue mushrooms if desired
Chill before serving