Preheat oven to 180°C and grease and line a Swiss roll tin with baking paper.
Add the eggs and caster sugar to a large bowl, whisk with an electric whisk until pale and frothy. In a separate bowl mix gluten free plain flour, baking powder, xanthan gum and cocoa powder. Gently fold the dry mixture into the wet mixture until combined.
Pour the mixture into your tin, spreading it out to the edges. Bake for 10 minutes until firm but still springy.
Remove from the oven and whilst it’s still warm, turn out onto another large sheet of baking paper sprinkled with a little icing sugar. Carefully peel the piece of baking paper off the bottom of the cake and trim the edges of the cake so they are straight.
Whilst the cake is still hot, tightly roll the sponge up from the short end with the baking paper inside it. Leave to cool completely.
Whilst the cake cools make the buttercream, by beating dairy free butter with an electric whisk until creamy. Slowy add the icing sugar and continue to whisk for up to 5 minutes until creamy and combined . Add the milk and vanilla extract whisk again until combined.
Carefully unroll the sponge and spread with a layer of the buttercream, roll back up.
Melt the dairy free chocolate and pour over the top of the log, smooth with a knife and leave to set.