IN a large saucepan sauté the yellow onions and green onions in the butter until softened. About 5 minutes. Then add the mushrooms and cook until tender. About 5 minutes. Add the asparagus, broth, water, salt, and pepper and simmer covered for about 20 minutes.
REMOVE the lid and puree the soup with a hand blender until it is a nearly perfectly smooth consistency. Then, add the rice and bring the soup to a boil for 2 minutes. Remove the soup from the heat and allow to cool for 5 minutes. Serve hot.