Preheat the oven to 350°. Spray a 9-by-2-inch round cake pan with cooking spray and line the bottom with parchment or wax paper. In a bowl, sift the cake flour with the 1/2 cup cocoa and the baking soda.
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.
Bake the chocolate cake for about 35 minutes, or until a cake tester inserted in the center comes out clean. Set the pan on a rack and let cool for 20 minutes. Invert the cake onto a large platter and let cool completely. (The chocolate cake can be kept, covered, at room temperature for 1 day.) Just before serving, garnish the cake by sifting the confectioners' sugar and the remaining 1 teaspoon cocoa evenly over the top.
One Serving Calories 258 kcal, Protein 4.5 gm, Carbohydrate 45 gm, Cholesterol 56 mg, Total Fat 7.8 gm, Saturated Fat 4.3 gm.