Cute story, TLT!
My family has a recipe that is similar, since my grandparents (on my dad's side) were born and raised in The Hague. Only, the boter koek recipe I am used to is more of a butter
cookie than a butter
cake. It turns out about the consistency of brownies, and involves separating egg yolks from egg whites, and brushing the whites on top just before you put it in the oven (converted to American measurements):
Dutch Boter Koek
4 1/3 Sticks Butter or Margarine (room temperature)
2½ Cups Sugar
4 Cups Flour
2 Egg yokes + some egg whites
Mix all ingredients EXCEPT egg white, until soft and smooth. Spread into 12 X 16 X 1 Jelly roll pan. Brush with egg white and bake on top rack for 15 min at 400 degrees F.