Preheat the oven to 180ºC/gas 4. Line a 26cm x 37cm swiss roll tin with baking paper, making sure it is higher than sides.
Blitz the walnuts in a food processor until finely ground, then add the baking powder and a pinch of sea salt.
Separate the eggs. Use an electric beater to whisk the egg whites to firm peaks. Gradually beat in half the sugar, till glossy.
In another bowl, whisk the egg yolks with the remaining sugar until pale and thick. Gently fold in the walnut mixture, flour and cocoa. Using a large metal spoon, fold the egg white mixture into the nut mixture, a little at a time. Spoon into the tin and bake for 25 minutes, until an inserted skewer comes out clean and the sponge is springy.
While still warm, lay a sheet of baking paper over the sponge and flip it out of the tin. Peel off the tin lining and leave to cool for 5 to 10 minutes. Drizzle the cake with the marsala and roll from the longest edge, the paper inside. Cover with a damp cloth.
Melt the chocolate in a bowl set over a pan of simmering water. Put the icing sugar in a food processor with the butter and blitz to cream. Add the slightly cooled chocolate and pulse till smooth. Place in a bowl and chill in the fridge for 30 minutes. Whisk the cream until just starting to peak and then gently stir in the chestnut purée.
When the sponge is cool, unroll and spread with the cream, leave a 2cm border around the edge. Re-roll the cake, without the paper but using it as a guide.
Spread the chocolate icing on top. Make wood-effect with a fork, then dust with icing sugar.