In a medium pot, bring 3 cups of chicken broth to a boil.
Add wild rice, reduce to a simmer, cover, and cook for 45-50 minutes, until al dente. Fluff with a fork and set aside.
In a large pot, heat olive oil and butter over medium heat.
Add onions, carrots, celery, and mushrooms. Season with onion powder, rosemary, thyme, salt, and pepper. Sauté for 5-6 minutes until softened. Add garlic for the last 30 seconds.
Sprinkle flour over the veggies and stir for 3 minutes to create a roux.
Gradually add 8 cups of chicken broth, stirring constantly. Bring to a boil, then reduce to a simmer for 15-20 minutes until thickened.
Add cooked wild rice, milk, and half-and-half. Simmer for 10-15 minutes.
Serve hot, making sure the soup is well-combined and heated through.