Preheat oven to 325F and lightly grease an 8x8 inch baking pan. Set aside.
Using a handheld electric mixer or a stand mixer fitted with the paddle attachment, beat the 4 egg yolks and the ¾ cup sugar on medium-high speed until the mixture turns light yellow (about 2 minutes).
Add ½ cup butter and 1 teaspoon vanilla and continue to beat until combined (another 2 minutes).
Add ¾ cup flour and mix well.
Gradually add the 2 cups milk and continue to mix until everything is fully incorporated. Set this batter aside.
In a separate bowl, using an electric mixer (you can also do this by hand if you're so inclined), beat the egg whites until you reach stiff peak.
Add your egg whites into your batter a third a time, gently whisking by hand each time, until the batter is smooth and no significant egg white streaks or lumps remain. Do not over-whisk.
Transfer the cake batter into your prepared pan and bake for 40-60 minutes or until the top of the cake turns golden brown.
Take the cake out of the oven, cool slightly then refrigerate overnight to chill and set completely.
Let the cake sit in room temperature for about 10 minutes before serving. Cut into squares, sprinkle with confectioner's sugar and enjoy.
The cake will look puffy straight out of the oven but will deflate accordingly as it cools.