Preheat your oven to 350°F (175°C).
Grease and line a 15x10 inch baking pan with parchment paper.
In a mixing bowl, whisk together eggs and sugar until pale and fluffy.
Sift in flour, cocoa powder, baking powder, and salt, gently folding with a spatula.
Pour the batter into the prepared pan, spreading evenly.
Bake for 12-15 minutes or until the cake springs back when touched.
Once baked, remove from the oven and let cool slightly before transferring to a clean kitchen towel dusted with powdered sugar.
Carefully roll the cake with the towel from the short side while still warm.
Let the rolled cake cool completely on a wire rack.
While the cake cools, prepare the ganache by melting the dark chocolate and unsalted butter together in a heatproof bowl.
Whip heavy cream with powdered sugar until soft peaks form.
Unroll the cooled cake gently, spread the whipped cream filling evenly, and reroll the cake tightly.
Trim the ends of the rolled cake slightly to create a clean edge.
Spread the ganache over the log cake and allow it to set.
Chill in the refrigerator for at least an hour before serving.