CAKE:
12 ounces bittersweet (not unsweetened) chocolate, chopped
3/4 cup unsalted butter, diced (1 1/2 sticks)
4 tablespoons granulated sugar (divided)
2 teaspoons ground fresh cardamon
7 large eggs, separated
SAUCE:
6 ounces bittersweet (not unsweetened) chocolate, chopped
3/4 cup half-and-half
1 tablespoon Grand Marnier or other orange-flavored liquer
To make cake: Butter an 8-inch springform pan. Line the pan with a sheet of parchment paper, then butter the paper. Preheat overn to 325 degrees.
Melt the chocolate and butter in a heavy saucepan over low heat, stirring constantly. When smooth, remove from heat and cool slightly. Stir together 2 tablespoons sugar with cardamon in a small bowl. Place egg yolks in a mixing bowl and, with an electric mixer on medium-high speed, beat them several seconds. Gradually add the sugar-and-cardamon mixture, then beat until the mixture has thickened and increased in volume, 2 to 3 minutes. Reduce speed to low, add the melted chocolate mixture and beat just to combine.
With an electric mixer with clean beaters on high speed, beat the egg whites until foamy, then gradually add remaining 2 tablespoons of sugar. Beat until soft peaks form, 1 to 2 minutes more. Stir or whisk 1 1/2 cups egg whites into the chocolate mixture to lighten it. Then fold in remaining egg whites in three equal additions. Spoon batter into prepared pan and bake on center rack of oven unitl cake puffs and top is set, 30 to 35 minutes. A tester inserted in the center will still be slightly wet. Cool to room temperature. Cake will deflate as it cools.
Run a knife around inside edge of pan and remove the sides. Carefully invert cake onto a serving plate, then remove and discard the parchment paper. Cover cake with foil or a cake dome and leave at cool room temperature. (Cake can be prepared one day ahead.)
To make sauce: Melt chocolate and half-and-half in a heavy suacepan over medium-low heat unitl smoooth. Add Grand Marnier or other liquer. (The sauce can be prepared a day ahead; cool, cover and refrigerate. Reheat over low heating, stirring.)
To serve: Dust the cake with podwered sugar. Slice cake and plave each serving on a dessert plate along with a scoop of ice cream. Drizzle both with warm sauce.