Creating the Bûche de Noël can be straightforward if you follow these simple steps:

1. Preheat Your Oven: Preheat your oven to 350°F (175°C). Line a 10×15-inch jelly roll pan with parchment paper and grease it lightly.
2. Prepare the Cake Batter: In a large mixing bowl, whisk the eggs and granulated sugar until pale and fluffy. Add the vanilla extract and mix well.
3. Combine Dry Ingredients: In another bowl, sift together the flour, cocoa powder, baking powder, and salt. Gradually fold the dry ingredients into the egg mixture until just combined.
4. Bake the Cake: Pour the batter into the prepared pan, spreading it evenly. Bake in the preheated oven for 15-20 minutes or until a toothpick inserted in the center comes out clean.
5. Cool the Cake: Once baked, remove the cake from the oven and let it cool in the pan for about 10 minutes. Then, carefully invert the cake onto a clean kitchen towel dusted with powdered sugar. Remove the parchment paper and roll the cake up with the towel, starting from the short end. Allow it to cool completely in the rolled position.
6. Make the Buttercream: While the cake is cooling, prepare the chocolate buttercream. In a large mixing bowl, beat the softened butter until creamy. Gradually add the powdered sugar and cocoa powder, mixing until smooth. Add the vanilla extract and enough heavy cream to achieve your desired consistency.
7. Assemble the Bûche de Noël: Once the cake is completely cool, unroll it carefully. Spread a generous layer of chocolate buttercream over the surface of the cake. Roll it back up gently without the towel, creating a log shape. Place the log seam-side down on a serving platter.
8. Frost the Log: Use the remaining buttercream to frost the outside of the rolled cake. You can use a spatula to create a bark-like texture for a more authentic look.
9. Decorate: Finish by adding chocolate shavings, fresh berries, or edible flowers as desired. Dust with powdered sugar for a snowy effect.
10. Chill and Serve: Refrigerate the Bûche de Noël for at least 30 minutes before slicing and serving to allow the flavors to meld.