1. Adjust an oven rack to the lower middle position and heat the oven to 325 degrees. Butter the sides of a 9 inch springform pan; flour the sides and tap out the excess. Line the bottom of the pan with a parchment or waxed paper round. Wrap the bottom and sides of the pan with a large sheet of foil.
2. Melt 12 tablespoons butter and the chocolates in a large bowl over a large saucepan containing about 2 quarts barely simmering water, stirring occasionally, until the chocolate mixture is smooth. Cool the mixture slightly, then whisk in the vanilla and egg yolks. Set the chocolate mixture aside, reserving the hot water, covered, in the saucepan.
3. In the clean bowl of a standing mixer fitted with the whisk attachment, beat the egg whites and salt at medium speed until frothy, about 30 seconds; add half of the crumbled brown sugar, beat at high speed until combined, about 30 seconds, then add the remaining brown sugar and continue to beat at high speed until soft peaks form when the whisk is lifted, about 2 minutes longer. Using a whisk, stir about one third of the beaten egg whites into the chocolate mixture to lighten it, then fold in the remaining egg whites in 2 additions, using the whisk. Gently scrape the batter into the prepared springform pan, set the springform pan in a large roasting pan, then pour the hot water from the saucepan into the roasting pan to a depth of 1 inch. Carefully slide the roasting pan into the oven; bake until the cake has risen, is firm around the edges, the center has just set, and an instant-read thermometer inserted into the center registers about 170 degrees, 45 to 55 minutes.
4. Remove the springform pan from the water bath, discard the foil, and cool on a wire rack 10 minutes. Run a thin-bladed paring knife between the sides of the pan and cake to loosen; cool the cake in the springform pan on a wire rack until barely warm, about 3 hours, then wrap the pan in plastic wrap and refrigerate until thoroughly chilled, at least 8 hours. (The cake can be refrigerated for up to 2 days.).
5. To unmold the cake, remove the sides of the pan. Slide a thin metal spatula between the cake and pan bottom to loosen, then invert the cake onto a large plate, peel off the parchment, and re-invert onto a serving platter. To serve, use a sharp, thin-bladed knife, dipping the knife in a pitcher of hot water and wiping the blade before each cut. (If you like, dust the cake with confectioners' sugar just before serving or top slices with a dollop of lightly sweetened whippped cream. To make slicing easier, freeze the cake for 30 minutes just before serving.).
Variation: Chocolate-Orange Mousse Cake. Follow the recipe for Bittersweet Chocolate Mousse Cake, reducing the vanilla extract to 1 teaspoon and adding 1 tablespoon orange liqueur and 1 tablespoon finely grated orange zest to the chocolate mixture along with the vanilla and egg yolks.