Preheat the oven to 325°F (160°C). Grease and line an 8-inch square baking pan with parchment paper.
Beat the egg whites in a clean bowl until stiff peaks form. Set aside.
In another bowl, beat the egg yolks and sugar until pale, thick, and creamy.
Add the melted butter and vanilla. Beat until smooth.
Add the flour and mix only until combined.
Slowly add the lukewarm milk while mixing on low speed. The batter will be very thin.
Fold the whipped egg whites into the batter in three additions. Do not overmix; a few egg white streaks are fine.
Pour the batter into the prepared baking pan.
Bake for 40 to 55 minutes, until the top is golden and the center does not jiggle when the pan is moved.
If the top browns too quickly, cover loosely with foil and continue baking until the center is set.
Cool in the pan for 1 hour. Refrigerate for 1 to 2 hours before slicing for cleaner squares.
Dust with powdered sugar and serve with cherries, strawberries, or whipped cream.