Lightly grease the slow cooker or add olive oil to the base.
Add potatoes, carrots, celery, onion, and garlic to the slow cooker.
Place the chicken on top of the vegetables.
Pour in the chicken broth and season with thyme, salt, and black pepper.
Cover and cook on LOW for 6–7 hours or HIGH for 3–4 hours, until the chicken is fully cooked and tender.
Remove the chicken, shred it with two forks, and return it to the slow cooker.
Stir in milk or cream. If a thicker soup is desired, mix cornstarch with water and stir it in.
Add frozen peas and cook on HIGH for an additional 10–15 minutes, until heated through and slightly thickened.
Taste and adjust seasoning before serving.