Place the chicken breasts directly into the slow cooker, then pour in the chicken broth, making sure the chicken is mostly covered. Add diced carrots, celery, thyme, and a pinch of salt and pepper. Cover with the lid and cook on low for 6 hours.
Once the cooking time is up, use two forks to shred the chicken into bite-sized pieces directly in the slow cooker. The chicken should be tender and easy to pull apart, with the vegetables softened.
Add the cream cheese chunks to the slow cooker and whisk gently to start melting it into the broth. Continue whisking until the mixture becomes smooth and creamy, about 5 minutes. The aroma will become rich and inviting.
If you'd like a thicker soup, dissolve the flour or cornstarch in a tablespoon of cold water to create a slurry. Stir the slurry into the soup and turn the slow cooker to high. Let it cook for another 10 minutes until thickened and bubbling gently.
Taste the soup and adjust the salt and pepper as needed. The soup should be velvety, fragrant, and steaming hot, with tender chicken and soft vegetables evenly distributed.
Turn off the slow cooker and let the soup rest for a few minutes. Ladle into bowls, garnish with fresh herbs if desired, and serve hot for a comforting, creamy meal.
