Sauté Vegetables: In a large pot or Dutch oven, heat the olive oil over medium heat. Add the diced onion, minced garlic, carrots, celery, and mushrooms. Sauté for about 5-7 minutes, or until the vegetables begin to soften.
Add Turkey and Rice: Stir in the shredded turkey and rinsed wild rice, mixing everything together well to incorporate flavors.
Pour in Broth: Add the chicken broth to the pot, followed by the dried thyme and rosemary. Season with salt and pepper to taste. Bring the mixture to a simmer.
Cook the Rice: Reduce the heat to low and cover the pot. Let it simmer for about 45-50 minutes, or until the wild rice is tender and has split open. Stir occasionally to prevent sticking.
Add Greens and Cream: Once the rice is cooked, stir in the chopped kale or spinach and heavy cream. Allow the soup to heat through for an additional 5-10 minutes.
Adjust Seasonings: Taste and adjust the seasoning with more salt and pepper as needed.
Serve: Ladle the hearty turkey and wild rice soup into bowls, garnishing with fresh parsley if desired. Enjoy warm with crusty bread or biscuits on the side!