Beat the egg whites briefly and add the cream of tartar. Continue to beat the egg whites until they are stiff and dry. Gradually beat in the cup of sugar and oneteaspoon of the vanilla extract.
Spread the mixture into a nine-inch pie plate and smooth it around with the back of the spoon until it resembles a piecrust. Place the shell in the oven and immediately turn off the heat. Leave the crust in the oven for at least four hours or overnight.
Whip the cream and add the remaining sugar and vanilla and the rum. Pour this filling into the baked shell and sprinkle with the grated chocolate. Chill and serve.