In a large soup pot or Dutch oven, heat the butter over medium heat. Add the onions, carrots, and celery, sautéing them until they become tender and golden brown.
Sprinkle the flour over the vegetables, stirring it in until the mixture is smooth and the raw flour cooks out, about 2 minutes.
Stir in the wild rice and chicken pieces, seasoning with salt and pepper. Pour in the chicken broth, ensuring everything is submerged, and bring the mixture to a gentle simmer. Let it cook for around 30 minutes, or until the wild rice is tender and cooked through.
Slowly drizzle in the heavy cream, stirring constantly to create a creamy, smooth texture.
Allow the soup to cook for an additional 5 minutes over medium-low heat, making sure the flavors meld together. Adjust seasoning with more salt and pepper if needed. Serve the soup hot, noting that it will thicken as it cools. Reheat it gently to loosen the broth before serving again.
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