For the banana-chocolate slices, beat the eggs with 3 tablespoons cold water, sugar and vanilla sugar until foamy. Fold in the oil, cocoa and flour and spread the batter into a baking pan lined with baking paper.
Bake in the oven at 180 degrees for 25 minutes. Let cool. Peel the bananas and cut them into slices about 3/4 cm thick, spread them close together on the cake.
Cook the pudding according to the recipe, pour over the cake and smooth down. Chill. Melt the chocolate in the microwave or in a water bath and spread over the cake.
Refrigerate the banana-chocolate slices before serving.