Line the Swiss roll tray with baking paper and preheat the oven to 200C (180C fan).
Put the eggs and caster sugar in a large mixing bowl. Whisk until thick, pale and considerably increased in volume.
Sift in the flour and cocoa. Fold through gently with a silicon spatula.
Tip the mixture into the lined tin and gently level off.
Bake for 8 minutes until just firm.
Shape the Swiss roll
Lay a rectangle of baking paper out on your counter. Sift the cocoa and icing sugar all over the paper.
Turn the hot Swiss roll sponge out onto the baking paper. Carefully peel off the paper backing.
Lay a clean teatowel on top of the Swiss roll sponge, then carefully roll the sponge up with the tea towel and baking paper. Leave rolled up to cool completely.
Make the frosting
You can make the frosting while the sponge is cooling. Melt the dark chocolate and set aside to cool.
Put the icing sugar, butter, vanilla and milk in a mixing bowl. Whisk together until pale, smooth and considerably increased in volume.
Add the cooled dark chocolate and whisk again to a smooth chocolate frosting.
Fill the Swiss roll
Carefully unroll the totally cooled sponge.
Spoon the frosting on top and spread to the edges.
Roll back up, this time without taking the baking paper with it.
Transfer to a serving board or plate, dust all over with cocoa and serve.
Any leftover chocolate Swiss roll should be transferred to a sealed container and placed somewhere cool, such as a pantry or cupboard, or in the fridge.It's important that the container is airtight as the sponge can easily dry out, and it's important that the storage area is cool as there is fresh butter in this recipe.