Preheat the oven 200 C / Gas 6. Grease and line a Swiss roll tin (9x13 in).
For the cake:
In a pan over barely simmering water, or in a double boiler, combine the sugar and eggs and whisk until lukewarm (be careful not to overheat the eggs). Remove from the heat and continue beating until the egg mixture is thick.
Gently stir in the sifted flour and cocoa powder being careful not to destroy the frothy appearance of the eggs. Pour the mix into the prepared cake tin and smooth to evenly fill the tin.
Bake in the preheated oven for 7 minutes or until springy to the touch. Remove from the oven and immediately place a sheet of baking parchment over the top, and a cutting board (this will help you to flip it).
Flip the tin and remove any baking parchment used to line the tin. Quickly and carefully roll up the sponge while still warm, leaving the top parchment in place, and rolling this up in the cake. Leave to cool thoroughly before proceeding.
For the filling:
Meanwhile make the filling. Put 3 tablespoons of boiling water into a bowl and melt into it into butter then add the vanilla extract. Gradually stir in the icing sugar (you may not need to use all of it); you want the mix to be thick but not stiff.
Carefully unroll the sponge and discard the baking parchment. Smooth the icing over the inner surface then re-roll the sponge.
For the outer icing:
Mix the outer Yule log icing by combining the ingredients and mixing until thick and creamy. Spoon over the rolled sponge to cover the cake and ends. Rough up the icing to imitate tree bark. Chill in the fridge for about an hour to set the icing.
Finally, dust with icing sugar and decorate if you wish. Slice and serve.