Cook the chicken. Place the chicken breasts in a slow cooker and cook on HIGH until fully cooked and the internal temperature reaches 165°F. Remove, shred with two forks, and set aside.
Sauté the vegetables. In a large Dutch oven, melt the butter over medium heat. Add the celery, carrots, onion, garlic, thyme, sea salt, and black pepper. Cook, stirring occasionally, for 8–10 minutes, until the vegetables begin to soften and become fragrant.
Make the roux. Sprinkle the flour over the vegetables and stir until evenly coated. Continue cooking for 2–3 minutes to eliminate the raw flour taste and create a lightly golden roux.
Add the broth and rice. Gradually pour in the bone broth, stirring continuously to incorporate the flour and prevent lumps. Add the wild rice and bring to a gentle boil. Reduce the heat to low, cover, and simmer for 40–50 minutes, or until the rice is tender, stirring occasionally.
Add the chicken. Stir in the shredded chicken and allow it to warm through for 3–5 minutes.
Finish with the cream. Reduce the heat to low and slowly stir in the whole milk and heavy cream. Warm gently for 3–5 minutes, stirring occasionally, until the soup is creamy and heated through. Avoid boiling once the dairy has been added.
Serve and enjoy! Taste and adjust the seasonings as needed. Ladle into bowls and serve warm.