Sift flours, confectioners' sugar, vanilla, and salt into the bowl of a standing mixer fitted with the paddle attachment. Add 4 1⁄2 tbsp. butter; mix on low until mixture has a sandy texture. Add egg and mix just until a dough forms. Shape dough into a disk, cover with plastic wrap, and refrigerate until firm, about 1 hour.
Heat oven to 350°. Grease an 8" fluted tart ring with a removable bottom with 1⁄2 tbsp. butter. Working on a lightly floured surface, roll dough into a 10" circle. Lay dough in tart ring and press it in to cover the bottom and sides. Trim off overhanging dough; prick the bottom all over with a fork. Cover the tart shell with plastic wrap and refrigerate for 30 minutes. Line tart shell with parchment paper, fill with dried beans or pie weights, and bake until the edges are lightly browned, about 15 minutes. Remove beans and parchment paper and bake until bottom is cooked through, 12–14 minutes more. Let the tart shell cool.
In a small pot, combine remaining butter, lemon juice, and 3⁄4 cup sugar. Heat over medium heat until bubbles form around the edges. Meanwhile, whisk 1 egg white, yolks, and 1⁄2 cup sugar in a large bowl until thick and pale, then whisk in the cornstarch. Drizzle hot lemon mixture into egg mixture while whisking constantly; strain through a fine sieve into a small pot. Cook lemon–egg mixture over medium heat, stirring constantly, until it's as thick as pudding, to make a lemon curd, about 10 minutes. Strain the lemon curd into a bowl, cover with plastic wrap, and chill in the refrigerator. Transfer chilled curd to the tart shell and smooth out to cover the bottom. Refrigerate the tart.
Heat 3⁄4 cup sugar and 1⁄4 cup water in a small pot over medium heat, without stirring, until it reaches 248° on a deep-fry thermometer (the firm ball stage) to make a syrup. Meanwhile, beat the remaining egg whites in a large bowl with an electric mixer until foamy. Add the remaining sugar and beat to soft peaks. Carefully drizzle the hot syrup into whites while beating constantly to make a meringue. Continue beating the meringue until completely cool.
Heat oven to 475°. Fill a pastry bag fitted with a saint-honoré tip with the cooled meringue. Pipe the meringue onto the tart, with the notch of the tip facing up, in a fan pattern, starting from the outside edge of the tart and working inward. Bake the tart until the top of the meringue is just lightly browned, about 2 minutes. Garnish the center with the lemon slice and refrigerate until chilled.