Add the olive oil, carrots, garlic, celery and onions to a 5-quart pot. Bring to medium heat and sauté 7-8 minutes.
Once the veggies are soft, add the flour and stir it in with the veggies. Add the broth, wil rice, seasonings and turkey. Bring the pot to a boil then cover, add the mushrooms and reduce to a medium-low simmer. Stir and for 20 minutes then serve!
Store the turkey soup in the refrigerator for 7 days or in the freezer up to 3 months.