Preheat your oven to 350°F (175°C). Line a 10×15-inch jelly roll pan with parchment paper and lightly grease it.
In a large bowl, whisk eggs and sugar until pale and fluffy (about 5 minutes with an electric mixer).
Add vanilla extract. Sift flour, cocoa powder, baking powder, and salt, then gently fold into the egg mixture.
Spread batter evenly in the prepared pan. Bake for 12-15 minutes, or until firm and springy.
Remove from the oven and turn onto a kitchen towel dusted with powdered sugar.
Peel off the parchment and roll the cake (with the towel) into a log. Cool completely.
Heat cream in a saucepan until simmering. Pour over chopped chocolate and stir until smooth.
Add butter and vanilla extract; mix well to create ganache.
Unroll the cooled cake, spread ganache over the surface, and leave a small border at the edges.
Re-roll the cake gently and transfer to a serving platter.
Coat the cake’s exterior with ganache, then use a fork to texture it like tree bark.
Dust with powdered sugar and add decorations for a festive touch.