Preheat oven to 180 degrees C. Line the bottom of a greased 23cm springform pan with baking paper. Grease the baking paper.
Separate the eggs.
In a food processor puree the chestnuts with the butter and the rum, scraping down the sides until the mixture is smooth. Add the melted chocolate and blend the mixture until it is combined well. With the motor running, add the yolks, 1 at a time and transfer the mixture to a large bowl.
In a bowl with an electric mixer beat the whites with the salt until they hold soft peaks, add the sugar a little at a time while beating, and beat the meringue until it holds stiff peaks.
Whisk about one quarter of the meringue into the chocolate mixture to lighten it and fold in the remaining meringue gently but thoroughly. Pour the batter into the prepared pan and smooth the top.
Bake the cake for 45 to 55 minutes or until a tester comes out with crumbs adhering to it and the top is cracked. Let the cake cool in the pan on a rack for 5 minutes, remove the side of the pan and invert the cake onto another rack. Remove the bottom of the pan, invert the cake onto a rack and let it cool completely. (The cake will fall as it cools.)
To Make Glaze: Put 185g of the finely chopped chocolate in a small bowl. In a saucepan bring 1/2 cup of the cream to a boil and pour it over the chocolate. Stir the mixture until the chocolate is melted and the glaze is smooth and stir in 1 tablespoon of the rum. Dip each glace chestnut halfway into the glaze to coat it partially, transfer the chestnuts to a foil-covered tray and let them set.
Invert the cake onto a rack set on greaseproof paper, pour the glaze over it, smoothing the glaze with a spatula and letting the excess drip down the side and let the cake stand for 2 hours or until the glaze is set. Transfer the cake carefully to a serving plate and garnish it with the coated chestnuts.
Make the whipped cream just before serving the cake: In a chilled bowl with chilled beaters beat the 1 cup cream until it holds soft peaks, beat in the 2 tablespoons sugar and the 1 tablespoon rum, and beat the mixture until it holds stiff peaks. Fold in the chopped glace chestnuts. Serve the cake with the whipped cream.