The Italians call it tronchetto di Natale, while the English say Yule log. But this traditional festive dessert originated in France, where it is called a bûche de Noël. Its log-like sponge represents the medieval tradition of burning the trunk of the Yule tree through the 12 days of Christmas. In this iteration, the creamy chocolate spread and addition of raspberries makes it a little lighter (but just as decadent) for an Australian climate.
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For sponge, preheat oven to 180˚C fan-forced. Grease and line a 25cm x 35cm Swiss roll tin or oven tray with baking paper. Whisk eggs in an electric mixer on medium-high speed until light and fluffy (6-8 minutes). Meanwhile, stir sugar and 1½ tbsp water in a small saucepan over high heat until sugar dissolves, then bring to the boil without stirring. With motor running, add hot syrup to eggs and whisk on medium speed until mixture cools and holds a thin ribbon (6 minutes).
Sieve in flour and cocoa, fold to combine, then fold in butter. Spread batter evenly in prepared tray and bake until sponge springs back when gently pressed (8-10 minutes).
Carefully turn out onto a clean tea towel lined with baking paper and dusted with cocoa and peel baking paper off base of sponge. Loosely roll sponge in tea towel, starting from a long edge, and leave to cool (30 minutes).
Meanwhile, for chocolate cream, heat chocolate in a heatproof bowl over a saucepan of simmering water, making sure the bowl doesn't touch water and stir frequently until melted (5 minutes); remove from heat and cool. Place butter in bowl of an electric mixer and beat on medium-high speed until smooth (30 seconds), then add cream cheese and beat on low speed until combined. Gradually add melted chocolate and beat until smooth; then add cream and beat until soft peaks form (5 minutes). Stand chocolate cream at room temperature until ready to assemble. (Do not refrigerate).
To assemble, using a small offset spatula, spread two-thirds of cream evenly over sponge, leaving a 2cm border along a long edge. Scatter raspberries evenly on top of cream, then roll cake up slowly.
Using a long spatula, transfer cake to a platter. Spoon remaining cream over the bûche de Noël. Scatter with chocolate shards, extra raspberries and slivered pistachios.