1. Simmer the prunes with the rum and 1 tablespoon of sugar in a small saucepan for a few minutes, until most of the liquid is absorbed. Remove from heat, cover, and let stand until cool.
2. To make the cake, preheat the oven to 325ºF (165ºC).
3. Butter a 9-inch (23cm) springform pan. Dust the inside with flour or cocoa powder, and tap out any excess.
4. In a large bowl set over a pan of simmering water, melt the chocolate and butter, stirring until smooth. Remove from heat and stir in the prunes and any liquid left in the pan.
5. Stir the egg yolks into the chocolate mixture.
6. In a separate bowl, or using a stand mixer, whip the egg whites with the salt until they begin to hold soft peaks. Continue whipping, adding the 3 tablespoons of sugar, one tablespoon at a time, until the whites hold their shape when you lift the whip.
7. Fold one-third of the beaten egg whites into the chocolate mixture thoroughly, then fold in the remaining egg whites just until no streaks of whites are visible. Don’t overfold.
8. Bake the cake for 40 to 45 minutes, or until the cake feels set close to the edges of the pan but the center is still rather soft to the touch and moist-looking. Let cool.
Serving: This cake is very moist, which makes it a bit challenging to get a clean slice out of it. Run a thin knife around the cake to loosen it from the pan and remove the springform mold. Dip the knife in very hot water then wipe the blade dry and use it to slice the cake, dipping the knife in the hot water and wiping it off between each cut.