In a large pot, heat up the olive oil over medium high heat. Add in the carrots, celery, and onion. Cook 2 to 3 minutes or until the onions are translucent and the carrots and celery are softened around the edges.
Add in the mushrooms, Italian seasoning, and garlic salt. Stir everything together and lower the heat to medium low.
Whisk in the all-purpose flour and cook for 4 minutes on medium low heat or until all the vegetables are thoroughly coated in the flour and fork tender. Stir occasionally so that nothing burns. This extra cooking will allow the soup to thicken up later.
Pour in the turkey broth and wild rice and bring to a boil on medium high heat. Reduce to a simmer on medium low heat.
Cover and let simmer for 40 to 50 minutes or until the wild rice has cooked through and is tender. Uncover and take soup off of heat.
Stir in leftover turkey and heavy cream. Let sit for 3 to 5 minutes or until the turkey is heated through. It shouldn’t take long. If needed, place the soup back on low heat until the turkey is heated.
Ladle into bowls and serve warm.