Grease an 8-inch square pan with butter or cooking spray. Line the pan with a layer of parchment paper covering the bottom and up 2 sides with a slight overhang. Lightly grease the parchment paper.
In a small saucepan, heat the milk and butter on low heat just until the butter melts. Don’t let the milk come to a boil or simmer. It should be warm but not scalding hot, 105 to 115°F. Set aside.
In a large bowl using a hand mixer, beat the egg whites on medium-high speed until they form stiff peaks, about 4 minutes.
In another large bowl, beat the egg yolks, sugar, vanilla extract, salt, and nutmeg (if using) on high speed until the mixture is pale and creamy, about 2 minutes.
Add the flour to the egg yolk mixture and beat on low speed until combined.
Continue mixing on low speed, or switch to a whisk, and pour in the warm milk and butter a splash at a time.
Add the beaten egg whites and use the whisk to gently mix until there are no large lumps of egg whites. Don’t overmix.
Pour the batter into the prepared pan. Bake until the top is golden brown, about 50 minutes.
Remove the pan from the oven and set it on a wire rack until it’s cool enough to go in the fridge, about 30 minutes.
Let the cake chill in the fridge for at least 1 hour before serving. Dust the top of the cake with powdered sugar, then slice it into squares.
