In a glass or ceramic bowl that is safe to use in the microwave, melt bittersweet chocolate in 15-second intervals, stirring after each one for one to three minutes. Transfer chocolate into the electric mixer's bowl.
Cut butter into pieces and beat into chocolate one piece at a time until incorporated. Add boiling water with sugar and beat. Beat in the eggs one at a time, slowly.
Fill the prepared cake pan with batter. Prepare a pan that is bigger than the cake pan; nestle the cake pan within the larger pan, then pour boiling water into the larger pan until halfway up the sides of the cake pan.
For forty-five minutes, bake the cake in the water bath in a preheated oven. Even so, the middle will appear damp. Put the cake in the fridge for eight hours or overnight, or until it is well cooled.
After dipping the bottom of the cake pan into boiling water for ten seconds, invert it onto a serving dish to remove the mold.