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Heat olive oil in a large pot over medium-high heat. Add onion, carrots and mushrooms and saute 3 minutes then add garlic and saute 1 minute longer.
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Add in chicken broth, chicken, oregano and thyme and season with salt and pepper.
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Bring to a boil, then reduce heat to medium-low, cover pot with lid and allow to simmer 10 – 15 minutes until chicken is cooked through (it should register 165 degrees in center on an instant read thermometer).
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While chicken is cooking, melt butter in a medium saucepan over medium heat. Add flour and cook, whisking constantly 1 minute.
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While whisking vigorously slowly pour in milk. Season with salt and pepper and bring mixture just to a light boil, stirring constantly. Remove from heat and set aside.
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Remove cooked chicken from soup and transfer to a cutting board, let rest 5 minutes then cut into pieces.
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Meanwhile, add tortellini to soup in pot, cover pot with lid and allow to boil over medium heat about 7 minutes (or time directed on package) adding in spinach during last 1 minute.
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Stir in chicken, white sauce and cream. Serve warm with parmesan cheese.