Joe Tilden's San Francisco Cream of Onion Soup

Melt butter in a heavy iron pot and stir in onion slices over low heat; cook slowly for at least 15 minutes, stirring often. Onions should be rich brown in color, without burning. Stir in stock and milk and add herbs. Cook at least 5 minutes to marry flavors. Just before serving, add the soup, a spoonful at a time, to beaten egg yolks; when this mixture is warm and well blended stir into soup and cook for 3 or 4 minutes to thicken. Cheese may be added just before ladling out soup, or served separately.