Preheat the oven to 350 degrees. Grease a 10-inch springform pan.
In the top of the double boiler over simmering water, combine the chocolate and butter. Heat until melted and smooth. Transfer to a medium-size bowl and whisk in the egg yolks and vanilla. Sift in the sugar, salt, and cocoa while continuing to whisk.
With a mixer, whip the egg whites to soft peaks. Fold one third of them into the chocolate mixture. Repeat with the remaining whites, then pour the mixture into the prepared pan. Place on the lower rack of the oven and bake for 25 minutes.
Remove to a cake rack and immediately loosen the springform collar (sides). Slip a plate inside the collar on top of the cake and push down slightly to push the air from the cake. Remove the plate and springform collar, and allow the cake to cool before serving.