Bring salted water to a boil. Add wild rice and return to a boil. Reduce heat and cover, simmering for anywhere between 25-55 minutes, until the rice has burst.
Meanwhile, in a heavy saucepan, heat olive oil. Cook onions, celery, and garlic. Once translucent, add in mushrooms. Let mushrooms cook down and release their juices, turning the mixture a nice deep brown color - about 20 minutes.
Add in oregano and flour and stir. Pour in wine and scrape the vegetables from the bottom of the pot. Let the mixture reduce a bit, then add in the cheese rinds, bay leaves, and broth.
Bring the soup to a boil, then reduce the heat and simmer for 20-25 minutes. Finally, add the rosemary, cream, cooked rice, and cider vinegar. Continue to simmer until soup has thickened, about 20 minutes. Salt and pepper to taste and serve.
Recipe by Things I Made Today at https://www.thingsimadetoday.com/2012/12/23/wild-rice-and-mushroom-soup/