Preheat your oven to 250°F (130°C). Grease a 12-inch (30cm) round cake pan that’s 3 inches (7.5cm) deep. Line the base with parchment paper.
Using an electric mixer, whisk the eggs with one-third of the sugar until the volume quadruples. This takes about 10 minutes.
While the eggs are whisking, melt the chocolate and butter together in a heatproof bowl set over a pan of barely simmering water. Make sure the water doesn’t touch the bottom of the bowl. Remove it from the heat once melted.
In a small pan, heat the remaining sugar with 9 fluid ounces (250ml) of water until the sugar dissolves completely, creating a syrup. Gently pour this syrup into the melted chocolate, stirring as you go.
Slowly add the warm chocolate and syrup mixture to the eggs while reducing the mixer’s speed. Keep beating until everything is well combined. The mixture might lose some volume, but that’s okay.
Pour this wonderful mixture into your prepared cake pan. Place the pan inside a larger baking pan on top of a dish towel (this keeps it stable). Fill the larger pan with hot water so it comes about two-thirds up the sides of the cake pan.
Bake for 1.5 to 2 hours or until the cake is set. You can check by gently placing your hand on the cake’s surface.
Take the cake pan out of the water and let the cake cool completely before removing it (don’t put it in the fridge). Serve it with a dollop of crème fraîche on the side.