Prepare the tin: Line a Swiss roll tin with parchment and preheat the oven to 200°C (400°F).

Whisk eggs and sugar: Beat eggs, sugar, and vanilla until pale, thick, and doubled in volume.

Fold in dry ingredients: Sift flour and cocoa into the mixture and fold gently to maintain the airiness.

Bake the sponge: Pour the batter into the tin, level the top, and bake for 8–10 minutes until springy to the touch.

Roll while warm: Turn the hot sponge onto parchment, peel off the lining, and roll tightly with the parchment inside. Allow it to cool rolled up.

Prepare the buttercream: Beat butter, cocoa, icing sugar, vanilla, and milk into a smooth, fluffy frosting.

Unroll and fill: Gently unroll the sponge, spread a layer of buttercream inside, and roll back up without squeezing out the filling.

Coat the log: Cover the outside with the remaining buttercream and drag a fork through it to create a bark-like texture.

Finish with decorations: Dust with icing sugar or add chocolate shavings for a snowy festive look.