Boil 10 cups water. Pour in tapioca and cook for 5 minutes, until tapioca becomes transparent. Remove and drain dry.
Boil 2 cups of water with 1 cup of sugar and cook for 3 minutes. Add butter and milk, thicken with cornstarch paste. Turn off heat, add vanilla extract and egg yolks. Stir quickly, then add tapioca. Mix well.