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In a large soup pot, melt the butter and olive oil over medium heat. Add the onion, carrot and celery and cook for 7-8 minutes or until onions are soft and translucent. Add the mushrooms and garlic and cook for 6-7 more minutes, until the mushrooms are cooked through.
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Sprinkle the flour on top of the vegetables, stir, and cook for 3-4 minutes, stirring frequently until flour is brown and cooked through.
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Add the chicken stock and soy sauce. Stir well to incorporate flour, then add the bay leaves. Over medium-high heat bring soup to a boil, then turn heat down to medium-low and simmer for 30 minutes.
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Add the wild rice and thyme and simmer for another 35 minutes.
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Add the chicken, milk, salt, pepper and cook on low for 20 more minutes.
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Serve hot in soup bowls with additional thyme if desired. Enjoy!