You can also add some dried mushrooms like oysters and porcinis. Reconstitute in boiling water for 30 minutes and reserve the juice for adding to the stock later as the soup cooks.
Rinse rice. Drain. Drop in boiling water with the salt. Reduce heat to medium and cook for 40 minutes or until water is absorbed and rice is tender. Check the pot and add some water if you need to. Wild rice can sometimes be a bit hard to cook.
Meanwhile, saute onions and celery in butter for about 10 mins or until onions start to turn brown. Add wine, reduce until there's about 2 T of liquid left. Add mushrooms and saute, stirring, for about 15 minutes. Add stock. If you saved juice from reconstituting mushrooms, add it. Reduce heat to low and allow to simmer uncovered for 20 minutes. Add rice and cream. Cook another 5 minutes. Add salt, pepper, and parsley if desired.