1. Preheat the oven to 375°F (190°C) and line a baking sheet with parchment paper.
2. In a mixing bowl, beat eggs and sugar until light and fluffy.
3. Sift together flour and cocoa powder, then gently fold into the egg mixture.
4. Spread the batter evenly onto the prepared baking sheet.
5. Bake for about 10-12 minutes until the sponge is set but not overbaked.
6. While the cake is baking, prepare a clean kitchen towel dusted with powdered sugar.
7. Once baked, carefully invert the cake onto the towel and peel off the parchment paper.
8. Roll the warm cake with the towel to prevent cracking and let it cool completely.
9. Prepare the filling by whipping heavy cream with sugar until soft peaks form.
10. Gently unroll the cooled cake and spread an even layer of filling over it.
11. Roll the cake back up tightly without applying too much pressure.
12. Prepare the chocolate ganache by heating heavy cream and pouring over chopped chocolate, then mix until smooth.
13. Spread the ganache over the rolled cake, covering it completely.
14. Use a fork or spatula to create a bark-like texture on the ganache.
15. Optionally, cut off a small section of the cake and attach it to the side to mimic a tree branch.
16. Decorate with powdered sugar, meringue mushrooms, sugared cranberries, and rosemary sprigs.
17. Allow the cake to set in the refrigerator for at least an hour before serving.
18. Slice and serve, enjoying your festive Chocolate Yule Log Cake.