In a medium stockpot, bring 3 cups of chicken broth to a boil. Add the wild rice, reduce to a simmer, cover, and cook until the rice is tender and slightly chewy, approximately 45-50 minutes. Stir occasionally and add additional broth if needed to prevent sticking. Once cooked, fluff the rice with a fork and set aside.

In a large stockpot, heat the olive oil and butter over medium heat. Add the finely chopped onion, carrots, celery, and sliced mushrooms. Season with salt, pepper, onion powder, rosemary, and thyme. Sauté for approximately 5-6 minutes, or until the vegetables begin to soften. Add the minced garlic during the final 30 seconds, stirring to release its aroma.

Sprinkle the flour evenly over the sautéed vegetables, stirring continuously for about 3 minutes to form a roux. This process will help thicken the soup.

Gradually add 8 cups of chicken broth to the vegetable mixture, stirring to combine. Increase the heat to bring the soup to a gentle boil, then reduce to a simmer. Allow the soup to cook for approximately 15-20 minutes, stirring occasionally, until it has thickened to your desired consistency.

Add the prepared wild rice to the soup, followed by the milk and half and half. Continue to simmer for an additional 10-15 minutes to allow the flavors to meld together. Adjust seasoning with salt and pepper as desired.

Ladle the soup into bowls while hot and serve immediately, garnished with additional herbs if desired.