In your slow cooker, add the rice, carrot, celery, mushroom, garlic, and chicken. Sprinkle both sides of the chicken with a pinch of salt and pepper.
Pour in the chicken broth and wine.
Sprinkle in your seasonings, and cover with the slow cooker lid.
Turn your slow cooker on either low heat for 6-8 hours, or high for 3-5 hours.
The chicken will be finished cooking before the rice. I checked my chicken after 3 hours of cooking. Cook until the chicken registers at 165 or is no longer pink in the middle. Put the chicken on a plate, cover with tin foil, and set aside.
Once the wild rice is fully cooked, shred the chicken with 2 forks (or your fingers) and return the chicken to the crockpot. Disregard the bay leaf. Plop in 4 tablespoons of butter, and gently mix until the butter is completely melted.
Taste for seasonings, see notes, ladle into soup bowls, garnish with fresh parsley or even cilantro, and enjoy!