Step 1

Heat the oven to 325°F with a rack in the middle position. Mist an 8-inch square metal baking pan or glass baking dish with cooking spray, then line it with a 7-by-16-inch sheet of kitchen parchment so the ends overhang the pan. Mist the parchment with cooking spray.

Step 2

In a 10-inch skillet over medium, cook the butter, occasionally swirling the pan, until the milk solids at the bottom are deeply browned and the butter has a rich, nutty aroma, 4 to 6 minutes. Transfer to a small bowl and cool until ready to use. In a small bowl, whisk together the flour and salt.

Step 3

In a stand mixer with the whisk attachment, beat the egg yolks and sugar on medium-high, scraping the bowl as needed, until the mixture is light, fluffy and doubled in volume, about 5 minutes.

Step 4

With the mixer running on low, slowly add the browned butter, then mix for 1 minute. With the mixer running, stream in the milk and vanilla; mix for 1 minute. Gradually add the flour, then mix until combined, about 30 seconds. The base will be thin and dotted with beads of flour; this is fine. Detach the bowl. Using the whisk attachment, scrape along the bottom and sides of the bowl to make sure no large pockets of flour remain, then transfer to a large bowl.

Step 5

Thoroughly wash and dry the mixer bowl and whisk attachment. Add the egg whites to the bowl then whisk on medium until foamy, about 1 minute. Increase to medium-high and whip until the whites hold stiff peaks, 3 to 5 minutes.

Step 6

Scrape the egg whites onto the batter, then fold in with a silicone spatula until the whites are broken into lumps about ½ inch in size; do not over-fold. The whites will not fully incorporate into the batter; the batter will remain fluid, with curd-like lumps of egg white at the surface.

Step 7

Gently pour the batter into the center of the prepared pan. Bake until puffed and deep golden brown, 45 to 50 minutes. Cool to room temperature in the pan on a wire rack, at least 2 hours; the cake will deflate slightly and pull away from the sides of the pan as it cools.

Step 8

Run a thin-bladed knife between the cake and pan to loosen. Using the parchment overhang as handles, lift the cake out of the pan and set it on a cutting board. Slide a thin metal spatula between the cake and parchment, then slide the parchment out from underneath. Cut the cake into pieces. Dust with powdered sugar just before serving.