Preheat oven to 325°F; grease bottom and sides of 9–inch springform pan. Line bottom of pan with parchment paper (See Notes). Dust side of pan with flour. Set pan on sheet of heavy-duty foil and wrap foil up the sides of pan to prevent water from leaking in during baking. (You may need to double-seam fold two sheets together to make a very wide piece of foil — you want the foil at least halfway up the sides of the springform.).
In a heavy saucepan over medium-high heat, dissolve 1/2 cup sugar in the water, stirring occasionally. Add chocolate and butter, stir until completely melted and mixed. Remove pan from heat and cool chocolate 15 – 30 minutes.
Meanwhile, beat eggs with remaining 1/2 cup sugar at high speed until mixture thickens and roughly triples in volume, about 6 – 8 minutes. Using a wire whisk, gently fold in the melted chocolate mixture, completely blending inches Take care to not deflate the whipped eggs. (See note).
Pour batter into springform pan and set inside a large roasting pan. Set an oven rack at the middle height in the oven and place the roasting pan on the rack. Pour enough boiling water in the roasting pan to come halfway up the side of the springform pan. (I angle a large pot lid over the springform to protect the cake from splashes or bad aim. School of hard knocks there, folks.).
Bake the cake for 25 – 35 minutes until the edges just begin to set and a thin crust forms on the top. Carefully remove the springform from the water bath and let cool on a rack. Cover and refrigerate overnight.
About 30 minutes before serving, remove from refrigerator, run a knife around the edges to loosen the pan, then remove the foil and side of springform. Invert on a plate, remove the parchment paper and turn cake right side up on a serving plate.