Preheat the oven to 375 degrees F. In a mixer fitted with the whisk attachment (or using a hand mixer), whip the egg whites until foamy. Add the cream of tartar and salt and continue whipping until soft peaks form. With the mixer running, gradually add 1 cup of the granulated sugar and continue whipping until stiff and the sugar has dissolved, about 30 seconds more.
Sift the remaining 1/4-cup of granulated sugar with the sifted cake flour 3 times, to aerate the mixture. Fold into the egg whites, then fold in the vanilla and maple syrup.
Spoon the batter into an ungreased proper angel food pan or 6 miniature ones. Smooth the top with the back of the spoon. Bake until light golden brown, 30 to 35 minutes. Cool by hanging the cake (in the pan) upside down around the neck of a bottle until it cools to room temperature. Run a long, sharp knife blade around the cake to loosen, then knock the cake out onto a plate.
Glaze: Stir the ingredients together until smooth. Pour over the top of the cake and spread with a spatula, letting the glaze trickle down the sides. Let set for at least 30 minutes before serving, or until the icing is hard. Cut with a serrated knife, using a sawing motion.
Consumption of raw or undercooked eggs, shellfish and meat may increase the risk of foodborne illness.
Recipe courtesy Gale Gand, "Butter Sugar Flour Eggs" by Gale Gand, Rick Tramonto, Julia Moskin: Clarkson N. Potter Publishers, 1999