1. Preheat the oven to 325°F (160°C). Grease an 8-inch square baking pan and line the bottom with parchment paper.
2. Separate the eggs, placing the yolks in a large mixing bowl and the whites in a clean bowl.
3. Beat the egg yolks and granulated sugar until lighter and creamy.
4. Add the melted and cooled butter and vanilla extract. Mix until well combined.
5. Sift the flour and salt over the egg yolk mixture. Whisk gently until incorporated.
6. Gradually pour in the lukewarm milk while whisking continuously. The batter will be very thin.
7. Beat the egg whites until soft peaks form.
8. Gently fold the whipped egg whites into the batter in two or three additions. Do not overmix; some wisps of egg white may remain visible.
9. Pour the batter into the prepared pan and gently smooth the surface.
10. Bake for 50–60 minutes, or until the top is lightly golden and the center has a slight jiggle.
11. Cool completely in the pan. Refrigerate for at least 2 hours for the cleanest slices and firmest custard layer.
12. Lift the cake from the pan using the parchment paper. Dust with powdered sugar, slice into squares, and serve chilled or slightly cool.