Melt the butter in a large pot over medium heat. Stir in the leeks and onion, and cook until tender.
Pour water into the pot. Mix in potatoes, carrots, asparagus, and rice. Season with salt. Bring to a boil, reduce heat, and simmer 30 minutes, until vegetables and rice are tender.
Stir spinach and heavy cream into the soup mixture, and continue cooking about 5 minutes before serving.
