1. Sauté Mushrooms: In a pan over medium-high heat, melt 2 tablespoons of butter. Add the sliced mushrooms and cook until they release their liquids and the liquid evaporates, about 10-15 minutes. Set aside.
2. Cook Vegetables: In the same pan, melt 1 tablespoon of butter. Add the diced onion, carrots, and celery, cooking until tender, about 8-10 minutes.
3. Add Aromatics: Stir in the garlic and thyme, cooking until fragrant, about 1 minute.
4. Simmer Soup: Add the chicken broth, wild rice, cooked chicken, and sautéed mushrooms. Bring to a boil, then reduce the heat and simmer, covered, until the rice is tender, about 20-30 minutes.
5. Finish with Cream: Stir in the milk and grated Parmesan cheese, cooking until the cheese melts. Season with salt and pepper to taste.

Optional Additions:

• For extra mushroom flavor, soak 1 ounce of dried mushrooms in 1 cup of boiled water for 20 minutes. Add the soaked mushrooms and their water along with the garlic.
• For a savory twist, add 2 tablespoons of white miso paste in step 5 before seasoning with salt and pepper.