Cook the Chicken:
In a large pot or Dutch oven, heat olive oil over medium heat. Season chicken with salt and pepper, then add to the pot. Sauté until cooked through, about 5-7 minutes. Remove and set aside.
Sauté Vegetables:
In the same pot, add onion, carrots, celery, and garlic. Sauté for 4-5 minutes until softened and fragrant.
Add Rice and Broth:
Stir in the rinsed wild rice, chicken broth, thyme, and bay leaf. Bring the mixture to a boil, then reduce heat, cover, and let simmer for 45-50 minutes, or until the rice is tender.
Make the Cream Base:
In a small bowl, whisk the flour into the milk (or half-and-half) until smooth. Gradually stir this mixture into the soup, and bring to a gentle simmer for 5-7 minutes, stirring until the soup thickens.
Combine and Finish:
Add the cooked chicken back into the pot. Adjust seasoning with additional salt and pepper if needed. Remove bay leaf.
Serve:
Ladle the soup into bowls and garnish with fresh parsley. Serve warm.