Preheat the oven to 325 degrees F. Line a 9-inch springform cake pan with parchment paper and spray the paper and the sides of the pan generously with nonstick cooking spray.
Set aside 3 tablespoons of the granulated sugar. Break the chocolate into pieces and place them in a large, heavy-bottomed pan along with the cubed butter and remaining sugar. Cook over LOW to MEDIUM-LOW heat until the chocolate and butter have melted, and the sugar has dissolved. Remove the pan from the heat. Stir in the vanilla, and leave the mixture to cool slightly.
While chocolate mixture is cooling, beat the egg whites in a large bowl with an electric mixer until foamy. Add the salt and beat until the mixture becomes puffy and white and you can see peaks when you pull the beaters out. Sprinkle reserved sugar over egg whites, and beat until stiff and glossy. Set aside.
Beat the egg yolks into the slighly cooled chocolate mixture one at a time, beating well after each addition. Beat in the flour just until combined.
Beat ⅓ of the egg whites into the chocolate mixture, then carefully fold in the remaining whites with a spoon or rubber spatula. Carefully pour the batter into the prepared pan, and tap the pan gently to release any air bubbles. Place the pan on a baking sheet.
Bake for about 35 minutes to 45 minutes, until well risen and the center feels almost set, but not completely. If the cake appears to rise unevenly, rotate after 20 to 25 minutes.
Remove from the oven, set the pan on a wire cooling rack, and remove the sides only. Do not attempt to remove the cake from the base before it's completely cooled as this cake is very fragile.
Sprinkle the completely cooled cake with confectioners' sugar. Remove from base, carefully peel off parchment paper and move to a serving platter.