Arrange alternate layers of bread and cheese in shallow 1 1/2-quart baking pan ending with a layer of cheese.
Heat milk with the onion.
Pour slowly over eggs combined with the seasonings, stirring constantly.
Pour milk mixture over bread and cheese.
Let stand for 5 minutes or longer.
Bake in preheated moderate oven (375°F.) for 20 minutes, or until pudding is set and bread and cheese are puffy.