Preheat the oven to 300°F (150°C). Grease a 10-inch round cake pan; set aside.

In a small saucepan over medium heat, combine sugar, water, and salt. Stir until completely dissolved; set aside.

Melt bittersweet chocolate in a microwave-safe glass or ceramic bowl in 15-second intervals, stirring after each interval, for 1 to 3 minutes. Pour melted chocolate into the bowl of an electric mixer.

Cut butter into pieces and beat them, one piece at a time, into the melted chocolate until combined. Beat in the hot sugar water. Slowly beat in eggs, one at a time.

Pour the batter into the prepared cake pan. Place the cake pan in a larger pan and fill the larger pan with boiling water halfway up the sides of the cake pan.

Bake the cake in the water bath in the preheated oven for 45 minutes. The center will still look wet. Transfer the cake to the refrigerator and chill thoroughly, 8 hours to overnight.

To unmold, dip the bottom of the cake pan in hot water for 10 seconds and invert onto a serving plate.