Place the eggs (while still in the shell) in a bowl of warm water. This will warm them up and help them whip to a higher volume. Let them sit while you prep the cake pans and the ingredients.
Preheat the oven to 350°F
Grease and flour two 8-inch square cake pans and place some parchment paper in the bottom of the pans.
Place the milk and butter in a saucepan and warm it over low heat until the butter melts. Keep the pan on the lowest heat setting to stay warm while you beat the eggs.
Crack the eggs in a large mixing bowl and add the sugar. Beat on high speed for about 8 to 15 minutes. The eggs should triple in volume and become pale yellow in color. (see notes)
Sift the flour, baking powder, and salt over the egg mixture and fold in with a spatula until it is just barely combined, you will still see some flour streaks.
Add the vanilla to the warm milk mixture and pour the milk in the batter. Stir the mixture by hand. Scrape the sides and bottom of the mixing bowl with a spatula to make sure all the flour is incorporated.
Divide the batter into the cake pans.
Bake for 30-34 minutes or until a toothpick comes out clean. Begin checking at 30 minutes.
When the cakes have finished baking, set the pans on a wire rack and let them cool in the pans.