1. Heat olive oil in a large pot over medium heat. Add the onion, garlic, carrots, and celery. Sauté until the vegetables are tender, about 5-7 minutes.
2. Add the cubed chicken to the pot, seasoning it with salt and pepper. Cook until the chicken is browned on all sides, approximately 5 minutes.
3. Stir in the wild rice and chicken broth. Bring the mixture to a boil, then reduce the heat to a simmer. Cover and cook for about 45 minutes, or until the wild rice is tender.
4. In a small bowl, whisk together the heavy cream and flour until smooth. Slowly add this mixture to the soup, stirring constantly to avoid lumps.
5. Simmer the soup for an additional 10 minutes, allowing it to thicken. Stir in the dried thyme, adjusting the seasoning with more salt and pepper if needed.
6. Serve hot, garnished with fresh parsley. Enjoy the warmth and comfort of this delicious soup, sharing it with loved ones just as I do with my family.

Remember, patience is key. Letting the rice simmer slowly allows all the flavors to meld beautifully, a tip I picked up from my family’s kitchen where time was always a secret ingredient.