Preheat the oven to 300 degrees F (150 degrees C). Grease a 10-inch round cake pan and set it aside.
In a small saucepan, combine the sugar, water, and salt. Heat the mixture over medium heat, stirring until completely dissolved. Set it aside.
Melt the bittersweet chocolate in a microwave-safe glass or ceramic bowl. Heat in 15-second intervals, stirring after each interval, for 1 to 3 minutes. Pour the melted chocolate into the bowl of an electric mixer.
Cut the butter into pieces and beat it into the chocolate, one piece at a time, until fully combined. Add the hot sugar water and beat until well combined. Slowly beat in the eggs, one at a time.
Pour the batter into the prepared cake pan. Place the pan in a larger pan and fill the larger pan with boiling water halfway up the sides of the cake pan. Bake in the oven for 45 minutes. The center will still look wet.
Place the cake in the refrigerator until thoroughly chilled, for at least 8 hours to overnight. To unmold, dip the bottom of the cake pan in hot water for 10 seconds and invert the cake onto a serving plate.
