To make the dough, in a stand mixer with the paddle attachment, mix the flour, sugar and salt on medium-low for 30 seconds. In a cup or small bowl, whisk the milk, yolks, lemon zest and yeast. With the mixer running, slowly add the milk-egg mixture; mix until evenly moistened, about 30 seconds. Increase to medium and beat until a sticky, cohesive dough forms, 2 to 3 minutes.

Scrape the bowl. With the mixer on medium-low, add the butter 1 piece at a time, mixing for 15 seconds between. When all the butter has been added, mix on medium, scraping the sides of the bowl and paddle as needed, until a very sticky, elastic, batter-like dough forms, 2 to 3 minutes. Remove the paddle and scrape off the dough that clings. Scrape the sides of the bowl and gather the dough at the center. Cover and let rise at room temperature for 1½ hours; the dough will not double.

Meanwhile, butter a 9-by-13-inch baking pan or glass baking dish, then line it with a 12-by-16-inch sheet of kitchen parchment so the ends overhang the long sides of the pan. Butter the parchment.

About 1 hour into rising, prepare the crème fraîche and semolina layers. To make the crème fraîche layer, in a medium bowl, combine all ingredients. Whisk until homogeneous; set aside.

To make the semolina layer, in a medium saucepan, combine the milk, sugar and salt. Bring to a simmer over medium, whisking, then reduce to low. While whisking, slowly stream in the semolina. Cook, whisking, until the mixture returns to a simmer (large bubbles burst on the surface) and is thick, smooth and resembles pudding, 2 to 3 minutes; a film will develop on the bottom of the saucepan. Transfer to a medium bowl. Using a silicone spatula, stir in the vanilla and lemon zest; cool until ready to use.

After the dough has risen 1½ hours, scrape it into the center of the prepared pan. Lightly flour your hands. Starting at center and using outstretched hands, gently press into an even layer to the edges and corners of the pan. Re-flour your hands as needed and press the dough firmly to remove as many air bubbles as possible. Do not pull or stretch the dough, which may cause it to tear, and be sure the edges are not thicker than the center. Let the dough rest, uncovered, for 30 minutes. Meanwhile, heat the oven to 400°F with a rack in the middle position. Thoroughly wash and dry the mixer bowl.

After the dough has rested for 30 minutes, add the egg whites to the clean mixer bowl. Using the whisk attachment, beat the whites on medium until frothy, about 1 minute. Increase to medium-high and whip until the whites are glossy and form soft, droopy peaks when the whisk attachment is lifted, about 3 minutes. Detach the bowl from the mixer.

Using a silicone spatula, stir the semolina mixture to loosen it slightly. Using the spatula, fold in one-third of the egg whites until mostly combined. Fold in the remaining egg whites until no streaks remain.

Gently pour the semolina mixture onto the center of the dough. Using the spatula, spread in an even layer to the edges. Slowly pour the crème fraîche mixture over it. Using the spatula, spread in an even layer that covers the semolina layer. Bake until the surface is spotty brown and just set but jiggles at the center when shaken, 35 to 40 minutes. Cool in the pan on a wire rack for about 30 minutes.

Run a thin-bladed knife between the cake and edges of the pan. Using the parchment overhang as handles, lift the cake out of the pan and set it on the rack; carefully slide the parchment out from underneath. Cool completely before serving. To serve, cut the cake lengthwise into quarters, then crosswise into quarters, forming 16 pieces. Dust with powdered sugar just before serving.