Sauté the Vegetables: In a large pot or Dutch oven, melt butter over medium heat. Add the onion, carrots, and celery. Cook for about 5 minutes until softened. Add the garlic, thyme, rosemary, salt, and pepper. Stir and cook for another minute.
Cook the Wild Rice: Add the wild rice and broth to the pot. Bring to a boil, then reduce heat and let simmer, covered, for about 45 minutes or until the rice is tender.
Add the Turkey: Stir in the cooked turkey and let it heat through for 5 minutes.
Make the Creamy Base: In a small bowl, whisk together the flour and milk until smooth. Slowly stir this mixture into the soup, followed by the heavy cream. Let it cook for another 5-10 minutes until the soup thickens.
Final Touches: Stir in the frozen peas (if using) and fresh parsley. Adjust seasoning to taste.
Serve and Enjoy: Ladle into bowls and serve warm with crusty bread or crackers.