Preheat the oven to 350 degrees F. Cut out a 8-inch round piece of parchment paper and place it in the bottom of an 8-inch springform pan. Butter the parchment and sides of the pan. Cover pan underneath and along sides with sheet of heavy-duty foil and set in large roasting pan. Bring a kettle of water to boil.
In the bowl of an electric mixer fitted with the whip attachment, beat eggs at medium-high speed until volume doubles, about 5 minutes. (At this point eggs will start to be slightly foamy)
Meanwhile, melt chocolate and butter in large heatproof bowl set over pan of simmering water, until smooth and very warm (about 115 degrees on an instant-read thermometer), stirring once or twice.
Fold 1/3 of egg foam into chocolate mixture using large rubber spatula until only a few streaks of egg are visible; fold in half of remaining foam, then last of remaining foam, until mixture is combined.
Pour batter into prepared springform pan and smooth surface with rubber spatula. Set roasting pan on oven rack and pour enough boiling water to come about halfway up side of springform pan. Bake until cake has risen slightly, edges are just beginning to set, a thin glazed crust (like a brownie) has formed on surface, and an instant read thermometer inserted halfway through center of cake registers 140 degrees, 22 to 25 minutes.
Remove cake pan from water bath and set on wire rack; cool to room temperature. Cover and refrigerate for at least 8 hours or overnight.
Remove springform pan sides, invert cake on a sheet of wax paper, remove parchment liner and turn cake right side up on a wire rack set over a rimmed baking sheet.