Prepare the Sponge Cake:
Preheat your oven to 350°F (175°C). Line a 10x15-inch jelly roll pan with parchment paper, ensuring the edges are covered.
In a bowl, sift together the flour, cocoa powder, baking powder, baking soda, and salt.
In a separate bowl, whisk the aquafaba until frothy. Add the sugar, plant-based milk, oil, vanilla extract, and apple cider vinegar. Mix until combined.
Gradually fold the dry ingredients into the wet mixture until just combined.
Pour the batter into the prepared pan and spread evenly. Bake for 10-12 minutes, or until the cake springs back when touched lightly.
Roll the Cake:
While the cake is still warm, carefully invert it onto a clean kitchen towel dusted with cocoa powder. Peel off the parchment paper.
Roll the cake gently with the towel, starting from the short end. Let it cool completely in the rolled shape.
Make the Filling:
In a chilled bowl, whip the coconut cream with powdered sugar and vanilla (and peppermint extract, if using) until fluffy.
Fill the Cake:
Unroll the cooled cake gently. Spread the whipped coconut cream evenly over the surface, leaving a small border around the edges.
Re-roll the cake tightly, using the towel to help. Place it seam-side down on a platter.
Prepare the Ganache:
Heat the coconut cream in a saucepan until just simmering. Pour it over the dark chocolate in a bowl and let sit for 2-3 minutes. Stir until smooth.
Let the ganache cool slightly, then spread it over the rolled cake. Use a fork to create a bark-like texture.
Decorate:
Arrange meringue mushrooms, sugared cranberries, and rosemary sprigs on and around the log. Dust with powdered sugar for a snowy effect.
Serve:
Refrigerate the Yule log for at least 1 hour before serving. Slice and enjoy this festive dessert!