Preheat oven to 350°F (175°C). Line the bottom of a greased 9-inch springform pan with parchment paper and grease the parchment.

Separate the eggs into yolks and whites.

Puree the chestnuts with butter and rum in a food processor until smooth. Add melted chocolate and blend. Incorporate egg yolks, one at a time, and transfer to a bowl.

Beat egg whites with salt until soft peaks form, gradually adding sugar. Continue beating until stiff peaks form.

Lighten the chestnut mixture by folding in a fourth of the meringue. Then gently fold in the remaining meringue thoroughly.

Pour batter into the prepared pan, smooth the top, and bake for 45 to 55 minutes. Let the cake cool for 5 minutes, remove from the pan, invert onto a rack, and cool completely.

For the glaze, combine chopped chocolate and boiled cream until smooth. Stir in rum. Dip each candied chestnut halfway into the glaze and let set. Pour glaze over the cake, smoothing it with a spatula. Let set for 2 hours.