Preheat the oven to 200°C, Fan oven 180°C, Gas Mark 6. Grease a 30x23cm Swiss roll tin with butter. Line with non-stick baking paper.
Melt the remaining butter, then set it aside to cool. Sift the flour, salt and cocoa powder together. Break the eggs into a separate large mixing bowl and whisk in the sugar using a hand-held electric mixer at the highest setting until very light and mousse-like. This will take 4-5 minutes to reach the right volume.
Fold in the flour mixture gently, using a large metal spoon. Next, fold in the cooled melted butter. Tip the mixture into the prepared tin and level the surface. (Do this quickly). Bake for 8-10 minutes, until the top springs back when touched lightly.
Put a large sheet of non-stick baking paper onto a work surface and turn the cooked cake onto it, while hot, so that it is upside down. Carefully peel off the lining paper. Roll up the cake from the short end with the baking paper (so that the paper is inside). Cool completely.
For the icing, whisk the butter and icing sugar together until light and creamy. Halve the mixture and whisk the cocoa powder into one half and the vanilla extract into the rest. Unroll the cake, spread with the vanilla icing and roll up carefully. Place on a serving plate and cover with the chocolate icing.
Spread the melted dark and white chocolate evenly over two chopping boards. Chill, then make chocolate curls with a large knife, pushing the knife away from you at an angle. Arrange on the cake with the chocolate eggs and sprinkle a little cocoa powder on top.
You could also make this log at Christmas by finishing it off with festive decorations.