Put the oil, butter, leeks, celery and onion in a large pot. Cover and cook about 8 minutes, stirring every minute or so, until the onion is translucent and the leeks have softened. Add the potatoes and water. Bring to a boil, lower the heat to medium, and cook until the potatoes are soft, about 12 to 15 minutes. Add the asparagus, milk and cream. Stir and cook, covered, at least 5 minutes longer. Season with salt and pepper, and sprinkle the chopped green onions on top of the soup just before serving. Wonderful soup!