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Preheat the oven to 350°. Butter two 9-inch round cake pans and line the bottoms with parchment paper. Butter the paper and dust the pans lightly with flour, tapping out any excess.
In a medium bowl, sift together the cake flour, baking powder and salt.
In the bowl of a standing mixer, beat the butter with the sugar at high speed until fluffy, about 5 minutes. Add the eggs and egg yolks, 1 at a time, beating well after each addition. Beat in the vanilla. Beat in the flour mixture at low speed in 3 batches, alternating with the milk; beat just until smooth.
Scrape the batter into the prepared pans and smooth the surfaces. Bake for 35 to 40 minutes, or until a toothpick inserted in the center of each cake comes out clean. Let the cakes cool on racks for 10 minutes, then unmold them onto the racks; let cool completely.
Fill a large bowl with ice water. In a heavy, medium saucepan, whisk the egg yolks with the sugar, lemon juice and salt. Add the butter and cook over moderate heat, stirring constantly, until the curd is thick and just beginning to simmer, about 5 minutes. Set the saucepan in the water bath and chill the curd, whisking occasionally.
In a saucepan, bring 1 inch of water to a boil. In the clean bowl of a standing mixer, whisk the sugar, egg whites and lemon juice. Set the bowl over the saucepan and cook, whisking constantly, until the sugar dissolves, about 6 minutes.
Return the bowl to the mixer and beat the meringue at medium speed for 10 minutes, or until cooled to room temperature. Continue beating at high speed until the meringue is thick, shiny and billowy, about 15 minutes longer.
Using a serrated knife, trim the cake tops to make them level. Halve each cake horizontally. Set 1 layer on a cake plate, cut side up, and spread it with one-third of the lemon curd. Set another layer on top and spread with another third of the curd. Repeat once more and then top with the final cake layer. With a large offset spatula, frost the side of the cake with a thin layer of the meringue. Top the cake with the remaining meringue and swirl decoratively, then serve.
The cake layers can be wrapped in plastic and refrigerated for 2 days or frozen for up to 1 month. The curd can be refrigerated for 3 days. The assembled cake can be refrigerated for up to 2 days.