Load the slow cooker. Add the chicken, wild rice, carrots, celery, onion, garlic, broth, and seasonings to the slow cooker.
Cook low and slow. Stir, cover, and cook on low for 6–8 hours or high for 3–4 hours, until the rice is tender and the chicken is cooked through.
Shred the chicken. Remove the chicken, shred it with two forks, and return it to the slow cooker.
Make the cream base. In a small saucepan, melt the butter, whisk in the flour, then slowly whisk in the cream to make a thickened sauce.
Bring it together. Stir the mixture into the soup and cook 15–20 minutes more to thicken.
Taste and serve. Adjust the seasoning as needed, then ladle into bowls and enjoy.