Melt the chocolate in a heatproof bowl set over a saucepan of simmering water, stirring occasionally. Remove from the heat and leave to cool for 5 minutes.
Put the egg yolks in a bowl, add the sugar and whisk together for 5 minutes until pale and very thick. Stir in the melted chocolate and the cocoa powder. Whisk the egg whites in a large clean bowl until stiff then fold into the chocolate mixture until evenly combined.
Transfer the mixture to an oiled and lined 33 x 23 cm (13 x 9 inch) Swiss roll tin, easing it well into the corners and spreading the surface level with a palette knife. Bake in a preheated oven, 180°C (350°F), Gas Mark 4, for 20 minutes until risen and set.
Meanwhile, cover a clean damp tea towel with nonstick baking paper and sprinkle with a little caster sugar. Quickly turn out the cooked sponge on to the paper. Carefully peel off the lining paper and cover the sponge with a clean tea towel. Leave to cool.
Make the filling. Blend the chestnut purée and icing sugar in a food processor until smooth. Transfer to a bowl and stir in the brandy. Slowly whisk in the cream until light and fluffy. Spread the filling over the sponge, leaving a 1 cm (½ inch) border all round. Starting with a short side and using the paper to help, roll up the sponge to form a log. Dust with icing sugar and serve.