Step 1

Preheat the oven to 180ºC, gas mark 4. Line the base of a 35x25cm Swiss roll tin with baking parchment, making sure to snip into the corners so the paper lies flat inside. Brush with a little vegetable oil. Use electric beaters to whisk the eggs with the sugar and salt until it quadruples in size and the mixture leaves a ribbon trail when the beaters are lifted out.

Step 2

Transfer a third of the egg mixture into a mixing bowl and roughly beat in the flour, cocoa powder and baking powder. Once totally incorporated, carefully fold in the remaining egg mixture until just combined. Tip the mixture into the prepared tin and cook for 15 minutes.

Step 3

Meanwhile, heat a large nonstick frying pan and add the chestnuts. Toast until golden all over, then add the sugar and turn the heat right down until the sugar has melted. Coat the chestnuts with the melted sugar until they’re glistening, then tip onto a large tray lined with baking parchment. Chill until cool and crunchy.

Step 4

When the sponge has cooked, remove it from the oven and flip it out onto a piece of baking parchment laid on top of a clean tea towel. Peel off the parchment from the top of the sponge. Carefully bring the long edge of the parchment underneath the sponge to the edge of the tea towel and roll it up tightly towards the other long edge. Place a second clean tea towel over the whole thing and tie the ends like a salami so that the sponge cools in that shape. Transfer to the fridge for 15 minutes.

Step 5

To make the filling, whip the double cream with all the other ingredients until the mixture is stiff. Remove the roulade from the fridge, unroll, and generously spread with the filling. Scatter over the caramelised chestnuts and carefully roll back into a sausage shape. Cut the end of the log diagonally and either reserve it for your ‘gift log’ (see tip, right), or stick it to the side of the main roulade, to make a Y-shaped log. Place back in the fridge while you make the buttercream icing.

Step 6

Beat the butter and gradually add the icing sugar until fluffy and doubled in size. Next, alternate beating in the cocoa and rum (or water) a little at a time until incorporated. Transfer to a piping bag with a large star nozzle. (If you don’t have a star nozzle, you can use a round one and finish by dragging a fork carefully across the surface to mimic the bark of a tree.)

Step 7

Pipe the buttercream, starting with a concentric circle at one end of the log. Next pipe big, long lines along the main part of the log until it’s completely covered. Repeat with the smaller section of the log. You can decorate it with rosemary twigs, upended to make ‘Christmas trees’. These look great with a little icing sugar sieved over the top. You can also decorate them with sprinkles – use a brush and a little icing sugar and water to glue them on. Keep the Bûche in the fridge for up to 24 hours – just take it out 30 minutes before serving.