Preheat oven to 300°F. Prepare one 10 inch round cake pan with nonstick spray and set aside.
In a small saucepan over medium heat combine the water, salt and sugar. Stir until completely dissolved and set aside.
Melt the bittersweet chocolate in the microwave for 1 minute, then in 15 second increments until mostly melted. Stir to combine any last bits.
Pour the chocolate into the bowl of an electric mixer.
Cut the butter into pieces and beat the butter into the chocolate, 1 piece at a time.
Beat in the hot sugar-water. Slowly add in the eggs.
Pour the batter into the prepared pan. Have a pan larger than the cake pan ready, put the cake pan in the larger pan and fill the pan with boiling water halfway up the sides of the cake pan (water bath method).
Bake cake in the water bath at 300°F (150°C) for 45 minutes. The center will still look wet. Chill cake overnight in the pan.
To unmold, dip the bottom of the cake pan in hot water for 10 seconds and invert onto a serving plate.