Chocolate Sponge Cake Rolled with Chestnut Cream

From 6 Bittersweets Guest Post
Adapted from Gourmet Traveller
Serves 6 to 8

XIAOLU'S NOTES: 
The homemade chestnut puree recipe makes more than you will need for this recipe. Extra puree can be refrigerated for up to 2 weeks and frozen for up to 1 year.

4 large eggs, room temperature
1/2 cup white sugar (preferably extra-fine/caster)
1/2 cup MINUS 1 Tbsp (65 g) cornstarch
5 Tbsp (35 g) Dutch-process cocoa, plus extra for dusting
1 Tbsp all purpose flour
1 tsp cream of tartar
1/2 tsp baking soda
3 1/2 Tbsp unsalted butter, melted and cooled
1 cup PLUS 2 Tbsp heavy cream
1 1/2 Tbsp powdered sugar, sifted
1 cup sweetened chestnut puree (Recipe below OR storebought is fine)

Preheat oven to 350 degrees F. Grease the base and sides a 12 x 16 3/4-inch jelly roll pan and line with parchment paper, cutting into the corners to fit and allowing the parchment to hang at least 3/4 inch past the tray's edges.

Whisk eggs and sugar using an electric mixer until thick and pale (about 5 to 6 minutes). Sift cornstarch, cocoa, flour, cream of tartar, and baking soda together into a separate bowl. Then gently fold dry ingredients into the egg mixture with a spatula. Fold in butter.

Spoon batter carefully into lined pan, smoothing the top with a spatula. Bake in the middle rack of the oven until the cake springs back when lightly pressed (10 to 12 minutes). Remove from oven and carefully turn cake out onto a tea towel lined with fresh parchment paper. Peel off the other parchment paper from the cake. With the short side facing you, roll the cake within the tea towel to form a log. Let stand until just cool (8 to 10 minutes).

Whip heavy cream and powdered sugar until soft peaks form (refrigerate if not using immediately). Unroll cake and spread it with an even layer of chestnut purée, then spread only the 1/2 of the cake closest to you with cream, leaving a 3/4 to 1-inch border around the other edges as well. Reroll, dust with cocoa powder, and serve immediately.

Homemade Sweetened Chestnut Puree
Adapted from Kopiaste (click over for great step-by-step photos)
Makes about 2 to 2 1/4 cups

400 g boiled and peeled chestnuts [I bought precooked vacuum-packed ones]
1 1/2 cups milk
3/4 cup sugar, or to taste
1 tsp pure vanilla extract

Fill a medium to large saucepan with 2 inches of water and bring to a simmer over medium heat. Place all ingredients EXCEPT vanilla into a large Pyrex glass or other heatproof bowl that has a rim wider than the saucepan and which will not touch the simmering water when placed over the saucepan. Cover with a heatproof lid and let mixture boil for about 1 hour, checking occasionally to stir and make sure milk does not boil over.

Drain and reserve milk and let chestnuts cool slightly. Puree the chestnuts using a potato masher or in a food processor. Mix vanilla into the reserved milk, then add milk back into the puree a tablespoon at a time until desired consistency and sweetness is reached. Allow to cool completely, then refrigerate or freeze until needed.