Adjust oven rack to lower-middle position and preheat oven to 325 degrees F. Grease 8-inch springform pan, line the bottom and sides with parchment, then grease the parchment. Wrap the outside of the pan with a double layer of aluminum foil and place in a 9x13-inch pan. Put a small pot of water on to boil.
Using a stand mixer with a whisk attachment, beat the eggs on medium speed until doubled in volume, about 5 minutes.
Meanwhile, place the chocolate, butter and coffee in a large, heat-proof bowl set over a saucepan of barely simmering water. Stir occasionally until completely melted and smooth and very warm (the mixture should register 115 degrees F on an instant-read thermometer). Remove from the heat and stir in the salt and vanilla extract.
Using a large rubber spatula, fold one-third of the eggs into the chocolate mixture until just a few streaks of egg are visible. Add the remaining eggs in two more additions, folding until the mixture is totally combined.
Transfer the batter to the prepared springform pan and smooth the top. Pour enough boiling water into the 9x13-inch pan 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 and a thin glaze (like a brownie crust) has formed on the surface, about 22 to 25 minutes. The cake should register 140 degrees on a digital thermometer.
Remove the cake from the water bath and set on a wire rack to cool completely to room temperature. Once cool, cover with plastic wrap and refrigerate at least 6 hours, or overnight (the cake can be refrigerated for up to 4 days).
About 30 minutes before serving, run a thin knife between the cake and sides of the pan; remove the sides of the pan. Place the cake on a serving platter, dust with powdered sugar and serve with a dollop of fresh whipped cream, if desired.