1. Preheat the oven to 200C/gas 6 and line a large baking sheet with baking parchment.
2. To make the meringue, pour the sugar onto the sheet and spread it out in an even layer. Warm in the oven for 5-6 minutes, until it feels hot to the touch and the very edges of the sugar are starting to melt.
3. While the sugar is heating up, put the egg whites into a large clean and grease-free bowl or the bowl of a stand mixer. With an electric hand whisk or in the stand mixer, whisk the whites until they form stiff peaks. You should be able to tip the bowl upside down without anything falling out – when you can do this you know it is ready.
4. Carefully whisk the hot sugar into the egg whites, adding a spoonful at a time and fully mixing in each one before adding the next. Avoid using any of the melted sugar from the edges of the baking sheet – this will not dissolve properly.
5. When all the sugar has been added, turn the mixer speed up and whisk for 8-10 minutes or until the mixture is really thick and glossy. If you rub a small amount between your fingers, you shouldn’t be able to feel any grains of sugar but, if it still feels gritty, continue to whisk for a few more minutes until it feels smooth. Sift the cocoa powder over the top of the meringue and fold in as gently as possible.
6. Turn down the oven to 120C/the lowest gas mark. With a pencil, mark four 20cm circles on the underside of a large piece of baking parchment, then place it on a baking tray with the pencil marks facing down.
7. Divide the meringue mixture evenly between the four circle stencils on the baking parchment and use a spatula to spread it right to the outside of the circles. Dust the top with a little more cocoa powder and bake for 1½ hours until crisp. To ensure a crunchy shell and soft, chewy middle, turn the oven off and leave the meringue to cool in the oven overnight. Alternatively, just leave it to cool on the tray until completely cold.
8. To make the filling, whisk together the chestnut purée, double cream, and icing sugar until the mixture forms soft peaks.
9. Place a meringue disc on a large plate and spread with quarter of the chestnut cream. Repeat with all four layers, then stack the discs on top of each other and sprinkle the chocolate curls over the top and serve immediately. You can store the dessert in the fridge for up to three days, but the longer you leave it the softer the meringue will become.