Begin by assembling all your ingredients. Preheat your oven to 300 degrees F. Lightly grease a 10-inch round cake pan and set it aside.
In a small saucepan, mix sugar, water, and salt over medium heat. Stir until the sugar and salt are fully dissolved, then remove from heat and set aside.
In a microwave-safe bowl, melt the bittersweet chocolate in 15-second bursts, stirring after each interval, until fully melted and smooth, usually taking 1 to 3 minutes. Transfer the melted chocolate to the bowl of an electric mixer.
Cut the butter into chunks and beat it into the chocolate, adding one piece at a time until the mixture is smooth.
Gradually mix in the hot sugar water, followed by the eggs, adding each egg one at a time and beating well after each addition.
Pour the batter into the prepared cake pan. Place this pan into a larger pan and pour boiling water into the larger pan until it reaches halfway up the sides of the cake pan.
Bake in the preheated oven for about 45 minutes. The center of the cake will still be slightly wet. Allow the cake to chill in the refrigerator for 8 hours or overnight to set completely.
To release the cake, briefly dip the bottom of the pan in hot water, then invert it onto a serving plate.