Bring stock and wine to boil in a pot. Stir in wild rice. Simmer covered until rice begins to split (about 45 minutes).
Heat olive oil and butter in large Dutch oven (if you don’t have a dutch oven, you can do this part in a large cast iron skillet and add it to the stock and wine instead of the other way around).
Saute onion in olive oil and butter about five minutes. Add mushrooms for 10 more minutes, stirring frequently.
When mushrooms and onions are done, sprinkle the flour over the mixture and then gradually add the cream. Add salt, pepper, thyme and nutmeg.
Pour stock, wine and rice mixture into Dutch oven. Stir and simmer for about 20 minutes. Serve immediately.