Combine olive oil and butter in a heavy stockpot over medium-high heat, then add onion, celery and garlic and cook until softened. Stir in curry powder and a pinch of salt and cook for a couple of minutes.
Add parsnips, thyme, mushrooms and stock and bring to a boil, then lower heat and gently simmer, partially covered, for about 30 minutes. Add wild rice and simmer, partially covered, for another 30 minutes.
Stir in buttermilk and cream, adding a little water if it needs thinning. Add salt and pepper to taste. Heat thoroughly and serve.