Mash the potatoes again until very smooth. Add the milk, salt, pepper, butter and onion and beat until fluffy. Stir in the cheese and add the beaten egg yolks. Beat the egg whites until they stand in soft peaks and carefully fold into potato mixture.
Turn into an ungreased one-quart casserole and bake for about one hour, until well puffed and firm in the center. Serve at once.