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In a Dutch Oven, heat the butter and olive oil over medium-high heat. Add in the celery, carrots, and onions, then sauté for 5 to 7 minutes.
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Stir in the garlic and cook for about 30 seconds, then add the flour and cook for another minute.
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Pour in the chicken broth and stir until the flour has dissolved, then add the Italian seasoning and chicken breasts. Bring the soup to a boil.
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Cover the soup slightly, leaving some room for steam to escape. Reduce the heat and simmer for 15 minutes.
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Remove the lid and stir in the orzo and cook for another 10 minutes or until the orzo is cooked through. Stir occasionally.
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Take the chicken out of the pot and shred it up, then add it back in. Add the lemon juice, parsley, and season the soup with salt & pepper as needed. Serve immediately.