In small skillet, heat 1 tablespoon butter. Add mushrooms and cook for 2 minutes over high flame, stirring constantly. Add 1/4 teaspoon salt and cayenne pepper. Sprinkle with flour and cook until slightly browned. Add chicken broth. Lower flame and simmer for 5 minutes.
Butter 4 curtard cups with remaining butter. Place 1 tablespoon mushrooms at bottom of each cup. Break 1 egg in each cup over mushrooms. Salt. Place cups in pan containing hot water. Bake at 400 degrees for approximately 10 minutes, or until white is well set. Serve hot.
(If eggs are taken from refrigerator just before cooking, baking time is about 5 minutes longer.)
Suggested Wine: A chilleddry white wine: Bordeaux Graves; etc.