Heat oven to 350° degrees. Position the oven rack in the lower center of the oven. Cover the outside of a 9-inch springform pan with a double layer of foil and lightly butter or oil.
Using a microwave oven or double boiler, melt together chocolate and butter; set aside to cool slightly.
In a bowl, whisk together egg yolks and 1/2 cup sugar until pale, frothy and increased in volume. Whisk in brandy, then fold in chocolate mixture. Place a kettle of water over heat, and bring it to a boil**.
Using an electric mixer, whisk egg whites and salt until thick. Add remaining 1/4 cup sugar, and continue to whisk until stiff and shiny but not dry.
Fold about 1/2 cup whisked egg whites into the chocolate mixture to lighten it. Gently fold in remaining whites, being careful not to let the mixture deflate.
Pour mixture into lightly-buttered springform pan, and place pan in a roasting pan. Add boiling water to the roasting pan to come halfway up the side of the springform pan. Bake for 45 minutes; top of cake will be hard and inside will be gooey.
Remove cake pan from water, and place on a rack to cool completely. Unwrap foil and remove side of springform pan. Place cake on a serving platter. Just before serving, dust top with confectioners' sugar passed through a sieve.