Adjust an oven rack to the lower-middle position and heat the oven to 325 degrees. Line the bottom of an 8-inch springform pan with parchment paper or waxed paper and grease the sides of the pan. (Be sure to grease the sides really well!) Wrap the outside of the pan with 2 sheets of heavy-duty aluminum foil and set it in a large roasting pan, or any pan that's larger than the springform. Bring a kettle or pot of water to boil.
In a stand mixer using the whisk attachment, beat the eggs at high speed until the volume doubles. This usually takes about 5 minutes.
Meanwhile, melt the chocolate and butter together. You can either do this in a double boiler on the stove (by placing the chocolate and butter in a large heatproof bowl, set over a pan of almost-simmering water, and stirring until melted and smooth). Or you can do this in the microwave (by heating the chocolate and butter in a microwave-safe bowl in 30-second intervals, stirring in between, until the chocolate and butter are melted and smooth). Then fold about a third of the beaten eggs into the chocolate mixture using a large rubber spatula until only a few streaks of egg are visible. Fold in half of the remaining egg foam, and then the last half of the foam, until the mixture is totally homogenous.
Scrape the batter into the prepared springform pan and smooth the surface with a rubber spatula. Place the roasting pan on the oven rack and VERY carefully pour in enough boiling water to come about halfway up the sides of the springform pan. Bake until the cake has risen slightly, the edges are just beginning to set, a thin-glazed crust (like a brownie) has formed on the surface, and an instant-read thermometer inserted halfway into the center reads 140° F, 22-25 minutes. Remove the springform pan from the water bath and set on a wire rack; cool to room temperature. Cover and refrigerate until cool. (The cake can be refrigerated for up to 4 days.)
About 30 minutes prior to serving, carefully remove the sides of the springform pan, invert the cake onto a sheet of waxed paper, peel off the parchment paper, and reinvert the cake onto a serving platter. If desired, top with berries. To slice, use a sharp, thin-bladed knife, dipping the knife into a pitcher of hot water and wiping the blade before each cut.