Rinse the wild rice and begin simmering it until slightly tender.
Sauté the mushrooms, onions, garlic, carrots, and celery in butter until softened.
Add the flour to create a roux and stir until fully combined.
Slowly whisk in the chicken broth and bring the mixture to a gentle simmer.
Stir in the cooked wild rice and shredded chicken.
Lower the heat and pour in the cream, stirring gently to combine.
Season with thyme, rosemary, salt, and pepper, then adjust to taste.
Simmer until the soup thickens and all ingredients are tender.
Finish with parsley and serve warm.