Place the egg whites in a mixing bowl. (Reserve the egg yolks for the buttercream, below.) Add the cream of tartar and beat until frothy. Gradually add three-quarters cup granulated sugar while beating. Continue to beat the meringue until it stands in stiff peaks when the beater is withdrawn from the mixing bowl.
Blend the remaining sugar, the almonds, zwieback crumbs, flour, cornstarch, and vanilla. Fold the mixture into the meringue.
Cut out two eight-inch circles of parchment paper and place them on a baking sheet. Or grease and flour a baking sheet and mark two eight-inch rings on it with the help of a layer-cake pan.
Spoon the meringue mixture into a pastry bag fitted with a plain tube with a half-inch opening. Pipe the mixture out spirally from the center to cover the prepared circles. Bake the layers for forty-five minutes. Cool.
Spread the buttercream between the cooled layers. Sprinkle sifted confectioners’ sugar and shaved chocolate over the top.