Combine mayonnaise, salt, pepper, and Worcestershire sauce.
Gradually add milk, stirring till smooth.
Cook over low heat, stirring constantly, till cheese melts and mixture is thick and smooth, about 5 minutes.
Put 2 tablespoons cheese mixture in bottom of each of 6 custard cups.
Break an egg into each cup, then add another 2 tablespoons of cheese mixture to each.
Sprinkle additional cheese on top, if desired.
Place cups in shallow pan, filling pan to 1 inch with hot water.
Bake in moderate oven (350°) 25 to 30 minutes.