Prep the base: Add onion, carrots, celery, garlic, wild rice, thyme, parsley, bay leaf, salt, and pepper to the slow cooker.
Pour in the chicken broth and stir to combine.
Add the chicken: Nestle the chicken breasts or thighs on top. If using butter or olive oil, dot or drizzle it over the mixture for extra flavor.
Cook low and slow: Cover and cook on Low for 6–7 hours or on High for 3–4 hours, until the chicken is tender and the wild rice is cooked through but still slightly chewy.
Shred the chicken: Remove the chicken to a plate and shred it with two forks. Discard the bay leaf.
Return the shredded chicken to the slow cooker and stir.
Make it creamy (optional): For a thicker, creamier soup, whisk the cornstarch with the milk or half-and-half until smooth. Stir into the slow cooker, cover, and cook on High for another 15–20 minutes until lightly thickened.
Taste and finish: Adjust salt and pepper as needed. Add a squeeze of lemon juice for brightness and sprinkle with fresh parsley if you like.
Serve: Ladle into bowls and enjoy with crusty bread or a simple green salad.