Serve on top of toasted English muffins or homemade bread, or bring to the table in baking dishes.
Preheat oven to 350 degrees. Grease 4 individual baking dishes. Combine mayonnaise, seasonings, and Worcestershire sauce in saucepan. Gradually add milk, stirring until smooth. Add cheese and cook over low heat until melted. Pour 2 tablespoons of sauce into each greased dish, add 2 eggs to each, and top with remaining sauce. Place dishes in pan of hot water ¼ inch deep and bake 12 to 15 minutes.