Wash and slice mushrooms, stems and all.
Saute in butter for 5 minutes.
Stir in flour, milk, bouillon, onion, salt, and pepper.
Cook, stirring, until thick.
Pour into individual shallow ramekins or a baking dish; sauce should be 1 inch deep.
Drop eggs into sauce, slipping a spoon under each egg so that it will sink slightly into the sauce.
Bake in a moderate oven (350°) until eggs are consistency desired