Must one cook a minimum of three eggs when all that is needed is just one egg?

In countries with modern farming methods, egg-laying hens are separated from males. It is therefore permitted to cook even one egg at a time without the worry that the pot may become not kosher (Shu"t Iggrot Moshe Yoreh Deah I 36- unless, for example, you raise your own roosters and hens in your backyard).