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1
Put oven rack in middle position and preheat oven to 325u00b0F. Butter sides of a 17- by 12- by 1-inch baking pan and line bottom with parchment paper. 3Sift flour with salt into a bowl.
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2
Beat egg whites in a large bowl with an electric mixer at high speed until they just hold soft peaks, then add granulated sugar, 1 tablespoon at a time, beating, and continue to beat until whites hold stiff, glossy peaks, 3 to 4 minutes in a stand mixer or 4 to 6 with a handheld. Add yolks and vanilla and beat until very thick, about 2 minutes.
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3
Sift flour mixture into egg mixture in 3 batches, folding in each batch gently but thoroughly. Spread batter evenly in lined baking pan.
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4
Bake until top of cake is pale golden and springs back when pressed lightly, 5 to 18 minutes. Cool cake in pan on a rack 5 minutes, then run a small knife around edges to loosen. Lightly dust top with confectioners sugar. Invert pan onto kitchen towel, then remove pan and peel off parchment. Cool cake completely, about 15 minutes.
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5
Whisk together cornstarch and milk in a 1-quart heavy saucepan until smooth. Bring to a boil over moderate heat, whisking constantly, then boil, whisking constantly, 1 minute. Whisk milk mixture gradually into egg yolk in a small bowl. Return mixture to saucepan and cook over moderate heat, whisking constantly, 1 minute. Transfer to a metal bowl, then put bowl into a larger bowl of ice and cold water and cool pastry cream, stirring occasionally, to room temperature, 6 to 8 minutes.
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6
Beat butter with confectioners sugar (1/4 cup) and vanilla in a medium bowl with cleaned beaters at medium speed until pale and fluffy, about 2 minutes. Beat cooled pastry cream, 1 tablespoon at a time, into butter mixture until smooth.
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7
Halve cake lengthwise, then transfer half to a cutting board and spread with all of pastry cream. Top with other half.
