Preheat oven to 325 F degrees. Grease and flour an 8x8 inch baking pan.
Separate the egg whites from the yolks. In a mixing bowl, beat the egg yolks with the sugar and water at high until light and creamy.
Add the melted butter, vanilla and a pinch of salt; continue beating until mixture is light and fluffy.
In a separate bowl, whisk together the flour and cocoa; add to the sugar/butter mixture in three batches, mixing thoroughly after each addition.
Once flour and cocoa powder has been mixed in, add the lukewarm milk a bit at a time and mix. The mixture should be liquidy. Set aside.
In a separate bowl, beat the egg whites and vinegar until stiff. Add the egg whites to the batter, a third at a time, gently folding in. Repeat until all egg whites has been folded in. The mixture should be thin like a pancake batter.
Pour the batter in the prepared baking pan. Using a spatula, gently give the batter one big stir and then bake for roughly 60 minutes. The cake will still jiggle in the middle when you take it out, so that's normal. Let it cool completely then cut into squares and serve.