Heat the oil in a Dutch oven over medium heat. Add the mushrooms, celery, carrots, and shallot and cook, stirring often, until softened—about 6 minutes. Stir in the flour, salt, and pepper and cook for 2 minutes more, stirring constantly. Add the white wine and thyme, then increase the heat to medium-high and cook for 2 minutes, or until the alcohol has cooked off.
Pour the broth into the Dutch oven and bring to a boil. Cover the pot, reduce heat, and simmer for 5–10 minutes, or until the vegetables are tender to your liking. Stir in the wild rice, sour cream, and parsley, then serve.
Notes
If you can find it at your grocery store, you can use instant wild rice instead of cooking your own. Add it just before covering the pot and reducing heat to a simmer.