Preheat oven to 350 degrees. Coat a 9-inch square baking pan with cooking spray. Line bottom with parchment cut to fit, and coat parchment with spray. Dust with flour, and tap out excess.
Whisk together eggs and sugar in a large heatproof bowl. Set bowl over a pan of simmering water, and whisk until mixture is warm and sugar has dissolved, about 3 minutes.
With a standing mixer fitted with the whisk attachment, beat egg mixture on high speed until pale and very thick, about 12 minutes. Beat in vanilla. Sift flour and salt over mixture in 3 additions, folding gently with a spatula. When almost incorporated, pour melted butter down side of bowl, and gently fold until completely incorporated.
Gently pour mixture into prepared pan. Bake until a toothpick inserted into center of cake comes out clean and top springs back when lightly touched, 30 to 35 minutes. Let cool completely in pan on a wire rack.
Invert cake onto rack, and remove parchment. (Cake can be wrapped tightly in plastic and refrigerated for up to 3 days or frozen for up to 1 month.) Using a serrated knife, cut cake horizontally into 3 layers.
Cake can be frozen for up to 1 month.