Preheat the oven to 350 degrees F and position a rack in the lower third of the oven. Butter the sides of a 9-inch round cake pan and dust them with flour, tapping out any excess. Line the bottom of the pan with a parchment paper circle and butter the paper. Line a rimmed baking sheet with parchment paper or aluminum foil.

In a standing mixer fitted with the whisk attachment, beat the eggs and 6 tablespoons sugar at high speed until they are thick, pale, and tripled in volume, about 5 minutes. (A handheld mixer may take longer.) Use a whisk to gently but thoroughly fold in the vanilla and flour. Spread the batter evenly in the prepared pan and bake until the cake pulls away from the sides of the pan and the top is golden brown and springs back when pressed lightly near the center, about 20 minutes. Set the pan on a rack until cool, about 20 minutes.

Run a knife around the edges of the cake to loosen it, then invert onto a plate. Remove the parchment paper. With a long serrated knife, cut the cake horizontally into 2 layers using a sawing motion. Place the layers on a flat surface and cut out 8 rounds using a 3-inch cutter. Arrange the rounds on the lined baking sheet. Place a generous scoop of sorbet atop each cake round. Transfer the sheet to the freezer and leave until sorbet is frozen solid, about 1 hour.

Beat the egg whites in an impeccably clean bowl with clean beaters at high speed until they are foamy and just beginning to form soft peaks. Add the 1/4 cup sugar a tablespoon or two at a time, allowing 30 seconds between additions, until it is completely incorporated, scraping the bowl as needed. Continue beating until the meringue is smooth, glossy, and holds stiff peaks.

Remove the cake rounds from the freezer. Working quickly to prevent the sorbet from melting, use a small spatula or knife to completely cover the sorbet and cake, making a good seal with the cake. Swirl the meringue decoratively. Return the baking sheet to the freezer for at least 20 minutes. (The assembled cakes can be frozen in an airtight container for up to 2 weeks.)

Preheat the oven to 500 degrees F and positlon a rack as low as possible. Transfer the baking sheet to the fully preheated oven and bake until the meringue is well browned, about 5 minutes. Serve immediately.