Adjust an oven rack to the lower third position but do not turn the oven on.
Put the whites into the bowl of a stand mixer. If whites are refrigerator temperature, let them wait at room temperature for 30 minutes to 1 hour until they’re about 60 degrees F
Sift the flour with ¾ cup of the sugar and the salt 4 or 5 times to aerate thoroughly.
Beat the whites on medium speed with the whip attachment for about 1 minute, until frothy. Entire surface will be bubbly. Stop the machine.
Pass the cream of tartar (which tends to be lumpy) through a small fine strainer into the whites and resume beating on medium speed until the whites form soft peaks. You’ll see traces of the beater blades in the whites.
On medium-low speed, gradually add ¾ cup of the sugar to the whites, about 1 tablespoon at a time, waiting about 10 seconds between additions.
Add the vanilla and increase the speed to medium high. Continue beating until the whites form stiff peaks that don’t droop at their tips.
Scrape the whites into a large wide bowl and sift one-fourth to one-fifth of the dry ingredients over the whites.
Fold together with the rubber spatula just until the dry ingredients are almost incorporated. Rotate the bowl as you cut down through the whites with the edge of the rubber spatula, sweep the spatula across the bottom of the bowl towards you, and bring the spatula up with a mound of whites.
Work quickly but gently. Repeat with the remaining dry ingredients, folding until the batter looks smooth.
Spoon the batter into the prepared pan, use a table knife to cut through the batter in concentric circles to cut large air bubbles, and smooth the top of the batter with the rubber spatula.
Put the cake in the oven and turn the oven on to 375 degrees.
Bake the cake about 35 minutes, until top is nicely browned with a few cracks and cake springs back when gently pressed.
Immediately turn the cake pan upside down over the neck of a wine bottle and let stand until completely cool, about 3 hours.
Remove cake from pan as described in the text. Cut into portions with a serrated knife.
Makes 12 to 16 servings.