Grease a 9-inch springform pan, and dust with unsweetened cocoa; set aside.
Melt chopped chocolate and butter in a heavy saucepan over low heat, stirring until smooth.
Whisk together egg yolks and vanilla in a large bowl. Gradually stir in chocolate mixture; whisk until well blended.
Beat egg whites at high speed with an electric mixer until soft peaks form. Gradually add sugar, beating until sugar dissolves and stiff peaks form. Fold one-third beaten egg white mixture into chocolate mixture; gently fold in remaining egg white mixture just until blended. Spoon batter into prepared pan, spreading evenly.
Bake at 375° for 25 minutes. (Do not overbake.) Let stand in pan on a wire rack 10 minutes before removing sides of pan.