Preheat the oven to 200˚C. Lightly butter a 20 × 30cm sponge roll tin and line the base and 2 sides with a piece of baking paper.
Beat the eggs, sugar and vanilla until pale yellow and very thick and fluffy. About 10 minutes.
Fold through the melted butter and hot water, and then sift on the flour, cocoa and baking powder. Fold gently through until the mixture is smooth and has no streaks.
Pour the mixture into a greased and lined 20 × 30cm sponge roll tin and bake for 10 to 12 minutes or until the cake springs back when lightly touched. While the cake is baking put a piece of baking paper on the bench, dusted with icing sugar.
Turn the cake onto the baking paper and spread it thinly with jam, then roll it up from a short side, using the baking paper to help it roll.
Leave the roll wrapped in the paper until cold, then unroll it and fill with whipped cream.
Reroll and either dust with icing sugar or cocoa, or spread it with chocolate butter Icing. Use a fork to make bark patterns in the icing and dust again with icing sugar to represent snow on the log. Chill for at least an hour before serving.