Preheat oven to 180 degrees C. Line a lamington tray (Swiss roll tray) with baking paper with heaps hanging over each end.
Whisk egg whites until soft peaks form, add about 1/3 of sugar and whisk in the sugar until they form firm peaks. In a second bowl whisk egg yolks and remaining sugar until it is moussy, pale, and thick, then add in the vanilla and sieve the cocoa over. Fold both in.
Lighten the yolk mix with a dollop or two of egg whites folding them in robustly, then add the remaining egg whites in thirds fold in carefully to avoid losing air. Pour cake mix evenly into the prepared lamington tray and bake for 20 minutes.
Let the cake cool before turning out onto another piece of baking paper dusted with a little icing sugar, it will help with sticking. Don’t worry too much about dents etc these will be covered with icing. Cover loosely with a tea towel.
Icing: Melt chocolate in a heatproof bowl in the microwave (I do it for 30 sec blocks on 80% power, stirring between each block) then let cool.
Put icing sugar and soft butter in mixer and process until smooth and combine then add cooled melted chocolate (if it isn’t cool the butter will separate - still tastes fine but it doesn’t look as nice).
Spread the prepared icing all over the cake going right out to the edges. Start the rolling with the long side facing you. Making sure you get a tight roll at the beginning, use the paper to roll the cake towards you.
Trim the end on an angle keeping the leftovers to make a branch. You get this effect by how you place that leftover cake against the main cake on an angle, making it look like a branch off a big log.
Spread the log with the remaining icing covering the ends and the branch well. To make the wood-like texture run a fork or skewer through the icing until you get the desired look you are after. Sprinkle with icing sugar to look like snow.