3/4 pound chestnuts, shelled
1/2 cup unsalted butter
4 tablespoons dark rum
10 squares (1-ounce) bittersweet chocolate, chopped
1/4 teaspoon salt
1/2 cup white sugar
6 squares (1-ounce) bittersweet
1/2 cup heavy cream
1 tablespoon dark rum
8 chestnuts, shelled
Preheat oven to 350 degrees. Line the bottom of a greased 9-inch spring form pan with parchment paper and grease the parchment paper.
Separate the eggs. In a food processor purée the chestnuts with the butter and the rum, scraping down the sides, until the mixture is smooth. Add the melted bittersweet chocolate and blend the mixture until it is combined well. With the motor running, add the yolks, one at a time, and transfer the mixture to a large bowl.
In a bowl, beat the whites with the salt with an electric mixer until they hold soft peaks. Add the sugar, a little at a time, beating, and beat the meringue until it holds stiff peaks.
Whisk about one fourth 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 in the center of the oven for 45 to 55 minutes, or until a tester comes out clean 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 onto another rack. Remove the bottom of the pan, invert the cake onto another rack and let it cool completely. The cake will fall as it cools.
For glaze: Put 6 ounces of the finely chopped chocolate in a small bowl. In a saucepan, bring the cream to a boil and pour it over the chocolate.
Stir until the chocolate is melted and the glaze is smooth; stir in the rum. Dip each chestnut halfway into the glaze to partially coat, then place nuts on a foil-covered tray to set.
Invert cake onto a serving plate and pour the glaze over the cake, smoothing with a spatula and letting the excess glaze drip down the side. Let stand for 2 hours or until the glaze is set.
Garnish with the coated chestnuts and serve.