Preheat the oven to 350ºF (180ºC). Have a 9-inch (23 cm) tube pan ready. (Do not use a non-stick tube pan.)
In a food processor coffee grinder or blender or food processor spin sugar until it is superfine.
Set aside 1 cup sugar. In a separate bowl, sift together the flour, 1/2 cup sugar, and salt, about three times.
In the bowl of an electric mixer, begin to whip the egg
whites on medium speed. When they become foamy, add the cream of tartar.
Increase the speed to high and continue to whip the egg whites until they just begin to hold their shape in soft, droopy peaks. Gradually whip the remaining 1 cup of sugar into the whites, 1/4 cup at a time. Do not overwhip; the egg whites should be soft and cloud-like. Mix in the vanilla.
With a rubber spatula, fold the flour and sugar mixture into the whites gradually, a small amount at a time.
Then fold the grated unsweetened chocolate just until incorporated.
Spoon the batter in the tube pan, smooth the top, and bake for 45 minutes. Remove from the oven and immediately invert the tube pan over a cooling rack. If the pan doesn’t have “feet”, set it over the neck of a heavy bottle or overturned metal funnel, using the center hole of the pan to hold the cake, until cool.
* If you don't have cake flour, substitute all-purpose flour less 2 tablespoons and replace it with potato flour or cornstarch.