Preheat your oven to 350°F (175°C). Line a 15x10 inch jelly roll pan with parchment paper and lightly grease it.
In a large mixing bowl, beat the eggs and granulated sugar until thick and pale, about 5 minutes. Add in the 1 teaspoon of vanilla extract and mix until just combined.
In another bowl, sift together the flour, cocoa powder, baking powder, and salt.
Carefully fold the dry ingredients into the egg mixture, making sure to keep the batter light and airy.
Pour the batter into the prepared jelly roll pan and spread it evenly. Bake for 12-15 minutes or until the cake bounces back when touched.
While the cake is baking, prepare a clean kitchen towel by sprinkling it with powdered sugar. Once the cake is done, remove it from the oven and immediately invert it onto the towel. Gently peel off the parchment paper and start rolling the cake (with the towel) from one short end to the other. Allow it to cool completely rolled up.
In a separate mixing bowl, whip the heavy cream, powdered sugar, and 1 teaspoon of vanilla extract until soft peaks form.
Once the cake is cooled, carefully unroll it. Spread the whipped cream mixture evenly over the cake, then roll it back up (without the towel this time) into a log shape.
For the frosting, take any leftover whipped cream or use a store-bought chocolate frosting of your choice. Frost the outside of the rolled cake.
Use a fork to create bark-like texture on the frosting. Sprinkle cocoa powder over the cake and garnish with dark chocolate shavings.
Refrigerate the Yule Log Cake for at least one hour to set before slicing. Cut into pieces and serve.
Notes
Chill the cake for at least one hour before serving for best results.