Preheat oven to 400° F (205° C). Oil Sheet Pan Liner and place on Sheet Pan.
In an electric mixer, whisk eggs and sugar on high for 5 minutes, until pale, thick, and doubled in volume.
Add water, vegetable oil, and vanilla. Sift in flour, cocoa, and baking powder, and fold very gently so that you do not lose any of the airy volume.
Carefully pour batter onto Sheet Pan Liner, spreading to all edges. Bake for 10–12 minutes, until pale golden brown.
While still warm, spread cake with Coconut Lime Sweet Dip.
Using the Sheet Pan Liner as a guide, starting at the short end, gently loosen cake while rolling snuggly into shape.
Sit the cake seam-side down.
Whisk icing sugar and cocoa, and cream with butter and salt.
Slowly beat in hot coffee for approximately 2 minutes, or until glossy. Stir in vanilla.
spread with mocha icing, garnish with pine branches and cranberries, and dust with icing sugar to look like snow.