Preheat oven to 175°C (350°F).
Line the bottom of a 20 cm (8-inch) springform pan with parchment paper. Lightly grease the sides.
Place the chopped dark chocolate and butter in a heatproof bowl.
Melt over a pot of gently simmering water (double boiler method) or microwave in 20–30 second intervals, stirring each time, until smooth.
Set aside to cool slightly.
In a large bowl, whisk the egg yolks and sugar together until pale and slightly thickened (about 2–3 minutes).
Add vanilla extract and salt. Mix.
Stir the melted chocolate mixture into the egg yolk mixture until smooth.
Fold in the chestnut purée until fully incorporated and creamy.
In a clean bowl, beat the egg whites until soft peaks form. The peaks should gently hold their shape but still look glossy.
Gently fold the whipped egg whites into the chocolate chestnut mixture in three additions.
Use slow, sweeping motions to keep the batter light. Do not overmix.
Pour the batter into the prepared pan and smooth the top.
Bake for 35–40 minutes, until the center is just set but still slightly soft. A toothpick inserted should come out with a few moist crumbs, not wet batter.
Let the cake cool completely in the pan.
It may slightly sink in the center — that’s normal for a flourless chestnut cake.
Remove from the pan. Dust with powdered sugar before serving.
Slice and serve at room temperature.