Cook the wild rice. Rinse the wild rice and cook it according to the package directions. Drain any excess liquid and set aside.
Sauté the vegetables. Melt the butter in a large Dutch oven or soup pot over medium heat. Add the onion, carrots, and celery, and cook for 5–6 minutes until softened.
Add the garlic and herbs. Stir in the minced garlic and thyme, and cook for about 30 seconds until fragrant.
Cook the mushrooms. Add the sliced mushrooms and cook for 8–10 minutes, stirring occasionally, until they release their moisture and become nicely browned.
Thicken the soup (optional). Sprinkle the flour over the vegetables and mushrooms. Stir continuously for 1 minute to cook out the raw flour taste.
Add the broth. Slowly pour in the broth while stirring to prevent lumps. Bring the soup to a gentle boil.
Combine the rice. Stir in the cooked wild rice and reduce the heat to a simmer. Cook for 10–15 minutes so the flavors can develop.
Finish with cream. Reduce the heat to low and stir in the heavy cream. Season with salt and black pepper. Heat gently without allowing the soup to boil.
Serve. Garnish with chopped fresh parsley and serve hot with crusty bread or a fresh green salad.