Βeat in a bowl the butter, the sugar and the vanilla until it becomes creamy.
Add the egg whites and beat until the mixture becomes uniform.
Add the warm milk and beat again for a while.
Next, combine the two mixtures and gently fold them together until they are well combined (do not use a mixer but an egg whisk).
In another bowl, sift the flour with the salt and the baking powder.
Combine the contents of the two bowls and mix them together until homogenized.
Place in a baking pan, either a round 24cm pan or 2-3 smaller rectangular pans, well buttered and floured.
Bake at 180°C for 30 minutes or until a toothpick inserted into the center of the cake comes out dry.
If you want to give the cake a bit of style and extra sweetness, serve it by sifting a little powdered sugar on top.