Make the chocolate chestnut mixture. Place 8.8 oz oz (250 g) sweetened chestnut purée and 5½ tbsp (80 g) unsalted butter in a small saucepan. Add 5.3 oz (150 g) dark chocolate (roughly chopped) and heat over low heat, stirring frequently, until everything has melted and the mixture is smooth.
Smooth the mixture if needed. If you can still see small pieces of chestnut purée, briefly beat the mixture with a hand mixer until smooth.
Chill the cake. Line a small round baking pan with parchment paper, leaving some paper hanging over the sides. Pour in the chocolate chestnut mixture and smooth the top.
Refrigerate. Chill for at least 4 hours, preferably overnight. The cake will become firm as the chocolate sets.
Make the caramel. Place 1 cup (200 g) granulated sugar in a small saucepan over low to medium-low heat. Let it melt slowly without stirring. You can gently swirl the pan if necessary. Continue until the sugar turns golden brown.
Add the butter. Carefully add 6 tbsp (85 g) unsalted butter (in cubes). The caramel will bubble vigorously. Whisk until the butter has melted and the mixture is smooth.
Add the cream. Slowly pour in ½ cup (120 ml) heavy cream while whisking. Be careful because the mixture will bubble and steam. Continue whisking until smooth, then let it boil gently for about 1 minute.
Season with salt. Remove the caramel from the heat and stir in Flaky sea salt to taste. Transfer to a heatproof jar and let cool.
Serve. Remove the cake from the refrigerator and let it sit at room temperature for 15–20 minutes. Cut into small wedges or squares and serve with salted caramel.