In a small saucepan, combine the granulated sugar, unsweetened chocolate, and 1/2 cup of water. Cook over moderate heat, stirring occasionally, until the sugar dissolves and the chocolate melts, about 4 minutes. Transfer the mixture to a large bowl and stir in the butter until melted. Stir in the buttermilk and vanilla. Beat in the eggs and egg white and then the flour mixture until combined. Pour the batter into the prepared cake pan.