Position a rack in the lower third of the oven; heat the oven to 325°F. Melt the butter in a small saucepan over medium-low heat and set it aside to cool. It must be no hotter than tepid when used.
Butter the bottom of a 10-inch springform pan and line it with a round of parchment or waxed paper; butter the paper. Dust the inside of the pan with all-purpose flour; knock out any excess. Sift the cake flour three times onto a sheet of waxed paper, return the flour to the sifter, and set the sifter on the waxed paper.
Beat the egg yolks until “ribbony”:
Using the whip attachment on your mixer, whip the yolks on medium-high speed until thickened, about 3 minutes. Continue beating on medium high and gradually add 1/2 cup of the sugar, about 2 Tbs. at a time; beat for 20 to 30 seconds between additions. You may need to stop to scrape the bowl occasionally. Beat on high speed until very thick and pale, about another 3 minutes. When the whip is raised, the yolks should fall into the bowl and form a slowly dissolving ribbon. Beat in the vanilla. Scrape the mixture into a large, wide bowl. Wash and dry the mixing bowl and the whip.
Whip the egg whites:
Combine the egg whites with the salt in the bowl of the mixer and begin mixing on medium low until frothy, about 1 minute. Increase the speed to medium and mix until the whip leaves distinct traces in the whites and forms peaks that curl softly at their tips when the beater is raised, about 4 minutes. With the mixer running on medium, gradually add the remaining 1/2 cup sugar, about 2 Tbs. at a time, beating for 20 to 30 seconds between additions. Continue beating on medium to medium-high speed until the whites hold a firm shape and form peaks that curl only very slightly at their tips, another 1 to 2 minutes. Don’t beat until the whites form stiff, unwavering upright peaks.
Check the melted butter to be sure it’s tepid (about 95°F) and liquid. The butter must not be at room temperature or it won’t blend into the batter properly. If necessary, rewarm it briefly.
Fold the whites into the yolks:
Scoop about a quarter of the whites over the yolk mixture and fold together gently with a few broad strokes of a large rubber spatula to lighten the mixture. Rotate the bowl a bit with each fold, and don’t be too thorough at this point: It’s all right if streaks of white remain. Sift about a third of the cake flour over the mixture and scoop about a third of the remaining whites over the flour. Fold together gently, turning the bowl as you go; but again, don’t be too thorough. Sift half of the remaining flour and scoop half of the remaining whites onto the batter and fold in the same manner. Sift on the last of the flour and add the last of the whites; fold gently but thoroughly, only until the batter is an even yellow color.
Fold in the melted butter:
Drizzle half of the tepid butter on top of the batter and partially incorporate it quickly with three or four broad strokes, turning the bowl a little with each fold. Pour on the remaining butter and fold it in only until no butter shows. Carefully scrape the batter into the prepared pan (the pan will be about half full), spread it evenly, and put the pan in the oven immediately.
Bake the cake:
Bake until the cake is golden brown and springs back when gently pressed, about 40 minutes; don’t overbake. Let the cake cool in the pan on a rack for 10 minutes. Run a sharp knife around the edge to release the cake from the sides; unclasp and remove the bottom of the pan and the paper liner. Replace the paper on the cake bottom and, cover with another rack, and invert. Let cool completely, right side up. If storing, wrap the cake tightly in plastic when completely cool.
Photo: Scott Phillips