Heat oven to 350ºF.
Take the sugar for a 2-minute spin in a food processor, then transfer half of it to a small mixing bowl and set aside. Add the flour and salt to the remaining sugar in the processor. Pulse several times to combine (and aerate). Set aside.
Whisk the egg whites and water in a large metal mixing bowl until the mixture just starts to foam. Add the cream of tartar and begin whipping with a hand mixer on medium speed for 1 minute. Add the extract of your choice and keep whipping on medium speed while very slowly adding the reserved sugar. Whip until all the sugar is incorporated and you’re looking at medium peaks. Play your cards right, and 3 minutes will do the trick. Add enough of the flour mixture to just dust the top of the foam. Fold it in using a rubber or silicone spatula and repeat until almost all of the flour mixture is incorporated.
Gently spoon the batter into an ungreased tube pan and bake for 35 minutes. Use a long wooden skewer to check for doneness, inserting it halfway between the inner and outer walls of the pan. If the skewer doesn’t come out dry, bake for 5 minutes longer.
Let the cake cool in the pan, upside down, for 2 to 3 hours before removing it from the pan and serving.