Cut a piece of greaseproof paper to fit the base of a swiss roll tin approximately 30x25cm.
Mix the eggs and caster sugar in a large bowl with an electric whisk for around ten minutes. The mixture will almost triple in volume and become paler in colour; it will be thick enough so that when you lift the whisk out of the mixture it will leave a visible trail on the surface.
Sift in the flour in three parts then very gently fold it in until the flour is blended in completely, it is important to go slowly and not to be too vigorous or you will lose some of the air in the sponge. Fold in a tablespoon of warm water.
Pour the mixture into the prepared tin and smooth it out evenly to the edges. Bake in the middle of the oven for 10 to 12 minutes until lightly golden and just firm to the touch.
Roll: Lay out a clean damp cloth or a couple of sheets of damp paper towel (this is to stop the paper slipping when you roll the cake). Place a large piece of greaseproof paper at least 5cm bigger than the cake onto the cloth. Sprinkle with 1 tablespoon of coconut.
In a large bowl, combine icing sugar and cocoa. In a saucepan, heat milk and butter until the butter is melted. Add the milk to the sugar mixture and mix well to create a fluid icing that is not too runny.
Loosen the sponge with a knife and ensure it can leave the pan easily. Then using a pastry brush paint the cocolate icing onto the cake, when well covered, cover with the coconut.
Quickly turn the cake onto the prepared paper; iced side down. You may need to support the sponge with your hand as your turn it out. Peel the paper off the sponge. Trim the edges so you have a tidy rectangle.
Using a spoon spread the buttercream evenly onto the sponge leaving about 2cm clear around the edges as the buttercream will spread when rolling.
Make a little incision into the edge of the surface of the sponge (not all the way through) about 1cm in from the end of the sponge (you will be rolling the shorter side inwards) and another cut opposite this on the other side. This just helps with the rolling.
Now you're ready to roll. The cuts at the edges are to help you start rolling. Use the paper to keep the roll tight; I find it best to the take the paper between your index finger and thumb and use the rest of your fingers to push the roll over. Leave the roll with the seam side down to cool.