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