In a large pot, heat olive oil over medium heat. Add onion, carrots, and celery. Sauté for 5-7 minutes until softened.
Add garlic, thyme, rosemary, and paprika. Cook for 1-2 minutes until fragrant.
Pour in the broth and stir in the wild rice. Bring to a boil, then reduce heat to a simmer. Cover and cook for 40-45 minutes until the rice is tender.
Stir in the cooked turkey and heavy cream. Simmer for another 5 minutes to heat through.
Season with salt and pepper to taste. Serve hot, garnished with parsley if desired.