Grease 2 deep 20cm loose-bottomed cake tins and line the base and sides with baking parchment. Heat oven to 160C/140C fan/ gas 3. Melt the chocolate and butter in a bowl over a pan of gently simmering water, then set aside to cool a little.
In a large bowl, whisk the whole eggs, yolks and sugars with an electric whisk until doubled in size – this will take about 5 mins. Sieve in the flour, cocoa and baking power with a pinch of salt. Fold the chestnut purée into the chocolate butter mixture, then add to the other bowl and gently fold everything together. Divide evenly between the tins.
Working quickly, clean the whisks and your large bowl, put the egg whites in the bowl and whisk until stiff. Add the sugar, a spoonful at a time, whisking continuously, until thick and able to hold stiff peaks. Use a spoon to dot the meringue on top of the cake mixture in both tins, then use the back of the spoon to spread the mixture. Fill the gaps to touch the edges of the tins – make nice swirly dips and peaks as you spread. Bake for 1 hr 15 mins until a skewer inserted into the middle of the cake comes out with moist
but set crumbs. Cool completely.
When you’re ready to serve, make the filling. Put the cream, chestnut purée and icing sugar in a bowl and whisk until softly whipped. Remove the cakes from their tins and place 1 on a cake stand or plate (save the one with the prettiest top for the final layer). Dollop on the cream and swirl out towards the edges (don’t worry if you crush the meringue a bit). Place the next sponge on top, dust with icing sugar, then top with chocolate shavings, if using. Best served straight away, but will keep in the fridge
for 2 days.