1 cup wild rice
1 large yellow onion, diced
4 celery stalks, diced
1 pound mushrooms, diced
2 cloves garlic, minced
1 teaspoon fresh oregano
3 tablespoons all-purpose flour
1 cup white wine
1 bay leaf
1 or 2 leftover cheese rinds, optional, for deeper flavor
4 cups vegetable or chicken stock
2 teaspoons minced fresh rosemary
1 cup whole milk or heavy cream
1 tablespoon cider vinegar
2 teaspoons salt, divided
Bring a pot of water to a boil. Add the wild rice and one teaspoon of salt, and reduce to a simmer. Cook for 40 to 50 minutes, until the rice has burst open and tastes tender. Drain, reserving the cooking liquid to use as stock, if desired.
While the rice cooks, prepare the rest of the soup. Warm a teaspoon of oil in a Dutch oven or stock pot over medium-high heat. Add the onions and celery with a half teaspoon of salt, and cook until the onions have softened and turned translucent, 3 to 5 minutes. Turn the heat down to medium and stir in the mushrooms and another half teaspoon of salt. Cook until the mushrooms have released all their liquid and turned dark golden-brown, 15 to 20 minutes. Don't skimp on this step! This is where the soup gets its deep, rich flavor.
Add the garlic and oregano, and cook until fragrant, about 30 seconds. Sprinkle the flour over the veggies and stir until the vegetables become sticky and there is no more visibly dry flour. Increase the heat again to medium-high and pour in the wine. Stir and scrape the brown bits from the bottom of the pan. Continue simmering until the wine has reduced by about half and the liquid has thickened a bit.
Add the bay leaf, cheese rinds (if using), and stock. Bring to a boil, then reduce to a simmer. Simmer for 20 minutes to meld the flavors. Add the rosemary, milk, and cooked wild rice. Simmer for another 10 to 15 minutes, until the soup has thickened to your liking. Stir in the cider vinegar. Taste and add more salt or vinegar to taste.
Leftovers will keep refrigerated for up to a week.