Preheat the oven to 200C/400F/Gas 6. Lightly grease a 33x23cm/13x9in Swiss roll tin, and line with non-stick paper or baking parchment, pushing it into the corners.
For the sponge, in a large bowl whisk the eggs and sugar using an electric hand whisk until the mixture is pale in colour, light and frothy. Sift the flour and cocoa powder into the bowl and carefully cut and fold together, using a spatula, until all the cocoa and flour are incorporated into the egg mixture. (Be careful not to beat any of the air out of the mixture).
Pour the mixture into the lined tin and spread evenly out into the corners. Bake in the middle of the preheated oven for 8–10 minutes, or until well risen and firm to the touch and the sides are shrinking away from the edge of the tin.
Place a piece of baking parchment bigger than the Swiss roll tin on the work surface. Dust with icing sugar generously. Carefully invert the cake onto the paper and remove the bottom lining piece of paper.
Cut a score mark 2.5cm/1in in along one of the longer edges. Starting with this edge, begin to tightly roll up the sponge using the paper. Roll with the paper inside and sit the roll on top of its outside edge to cool completely.
While the cake is cooling, make the ganache topping. Heat the cream in a pan, just so as you can keep your finger in it. Remove from the heat and add the chocolate, stirring until it is melted. Cool to room temperature, then put into the fridge to firm up (this icing needs to be very thick for piping).
Uncurl the cold Swiss roll and remove the paper. Spread the whipped cream on top, and re-roll tightly. Cut a quarter of the cake off from the end on the diagonal. Transfer the large piece of cake to a serving plate and angle the cut end in to the middle of the large cake to make a branch.
Put the chocolate icing into a piping bag fitted with a star nozzle. Pipe long thick lines along the cake, covering the cake completely so it looks like the bark of a tree. Cover each end with icing or, if you wish to see the cream, leave un-iced. Alternatively, just use a palette knife to spread on the icing and create rough bark texture with a fork.
Dust with icing sugar and garnish with fresh holly or a little robin to serve.