Preheat oven to 350. Place the bottom of a 9-inch round springform pan upside- down (concave side down); secure sides of pan. Butter pan; line sides of pan with a long strip of waxed or parchment paper, butter paper. Wrap bottom of pan securely in aluminum foil. Bring a kettle of water to a boil.
In a large heatproof bowl set over, not in, a pan of simmering water, melt chocolate; cool to room temperature.
Using an electric mixer on high beat eggs, sugar, salt and rum until thick and foamy and batter holds a trail, about 3 minutes
Stir half of the egg mixture into cooled chocolate to lighten it. Fold in remaining egg mixture and whipped cream. Spoon batter into prepared pan and smooth top.
Place pan in a roasting pan and pour hot water to come halfway up the sides of the pan. Bake until set and firm to the touch, 30 to 35 minutes. (It will look like a cheesecake.) Transfer to a wire rack to cool to room temperature, then refrigerate until well chilled, about 3 hours.
To serve: Release sides of springform and using a knife dipped in warm water, cut into thin slices.
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