Cake : Heat oven to 180°C with rack in middle. Butter a pan and line bottom and sides with a sheet of baking paper. Once the baking paper is in the tin, butter the baking paper and dust with additional flour, knocking out excess.
Beat together egg yolks, vanilla, and 1/2 cup Chelsea White Sugar in a large bowl with an electric mixer at high speed until thick and pale (5 to 8 minutes in a stand mixer or 8 to 12 minutes with a handheld). Sift half of flour over egg yolk mixture and fold it in gently, then sift and fold in remaining flour.
Beat egg whites with salt and cream of tartar in a large metal bowl at medium speed until they just hold soft peaks. Beat in remaining 2 tablespoons Chelsea White Sugar, 1/2 tablespoon at a time, and continue to beat until whites just hold stiff peaks.
Fold 1/4 of egg white mixture into egg yolk mixture to lighten, then fold in remaining egg white mixture gently but thoroughly.
Stir 1/2 cup of egg batter into melted butter in a medium bowl until combined, then fold butter mixture into egg batter gently but thoroughly. Spread batter evenly in sheet pan and tap once on counter to help eliminate air bubbles.
Bake until top of cake springs back when gently pressed with finger, 7 to 10 minutes.
Sift top of hot cake evenly with 2 tablespoons of Chelsea Icing Sugar and cover cake with a sheet of baking paper and a tea towel. Flip cake onto baking paper and tea towel. Carefully peel off the baking paper.
With the long side of the cake nearest you and using the tea towel as an aid, roll up cake in the baking paper, Swiss roll style, keeping it wrapped in towel. Cool cake completely, seam-side down in towel, on a rack. It can be cooled in the fridge for an hour to reduce the cooling time or 2-3 hours on a kitchen bench.
Espresso syrup: Bring espresso and Chelsea White Sugar to a boil in a small saucepan, stirring until Chelsea White Sugar dissolves, then boil until reduced to a 1/4 cup. Remove pan from heat and stir in Cognac, then cool to room temperature.
Filling: Slowly mix mascarpone, Chelsea White Sugar, cinnamon, and Cognac in a large bowl with an electric mixer until combined. If mixture is very loose after adding Chelsea White Sugar, beat mixture briefly to thicken slightly (see Cooks' notes).
Beat thickened cream in another bowl with same beaters at medium speed until it just holds stiff peaks. Fold whipped cream into mascarpone mixture.
Ganache: Heat thickened cream in a small saucepan over medium heat until it just comes to a boil, then pour over chocolate and let stand 3 minutes. Stir slowly with a whisk until smooth. If bits of chocolate remain unmelted, set bowl over a pan of barely simmering water and heat, stirring gently, until completely smooth, and remove from pan. Stir in corn syrup. Chill, stirring a couple of times, until it thickens to an easily spreadable consistency, about 15 to 20 minutes.
Assemble yule log: Gently unroll cooled cake on the sheet of baking paper wrapped around it, with the long side of cake nearest to you. Brush all the cooled espresso syrup all over surface of cake. Spread mascarpone filling with spatula evenly over cake, leaving a 1cm border all around.
Starting from long side nearest you, roll up the cake, leaving it seam-side down on baking sheet. Gently brush off any excess Chelsea Icing Sugar on the cake. Cut a 4cm long diagonal slice from one end of the cake roll and put aside. Transfer cake roll, using 2 flat spatulas as aids, seam-side down onto platter. Using ganache as "glue," attach the cut off end piece, flat end onto the middle of the main cake roll to resemble branches. Spread ganache all over cake roll and branches with offset spatula. Using a fork, scrap down the log, making it resemble tree bark (see Cooks' notes).
Arrange raspberries and leaves around log to decorate. Dust Chelsea Icing Sugar over log, raspberries and leaves to resemble a light dusting of snow.
Additional tips
Yule log can be made 1 day ahead and chilled, loosely covered with plastic wrap. Bring to room temperature before serving.
