Add the sliced mushrooms and cook for another 5 minutes until browned and their liquid has evaporated. Stir in the garlic and thyme, cooking for 1 minute until fragrant.
Sprinkle the flour over the vegetables and stir constantly for 1-2 minutes to cook out the raw flour taste.
Gradually pour in the chicken broth while whisking constantly to prevent lumps. Stir in the uncooked wild rice.
Bring the mixture to a boil, then reduce the heat to low. Cover and simmer for 40-50 minutes, or until the rice is tender.
Stir in the cooked chicken and heavy cream. Simmer gently (do not boil) for 5 minutes to heat everything through.
Season with salt and black pepper to taste. Serve hot with toasted bread.