Prep the base: Add the onion, carrots, celery, and garlic to the slow cooker. Sprinkle in the thyme, Italian seasoning, bay leaf, salt, and pepper.
Add chicken and liquid: Place the chicken on top of the vegetables. Pour in the chicken broth.
Cover and cook on Low for 6–7 hours or High for 3–4 hours, until the chicken is fully cooked and tender.
Shred the chicken: Remove the chicken to a cutting board and shred it with two forks. Discard the bay leaf. Return the shredded chicken to the slow cooker.
Thicken (optional): If you prefer a thicker soup, whisk the cornstarch into the half-and-half or cream until smooth.
Stir this mixture into the slow cooker.
Add gnocchi: Stir in the gnocchi and cook on High for 20–30 minutes, or until the gnocchi is tender and cooked through. Stir occasionally to prevent sticking.
Finish with greens and cheese: Add the spinach, Parmesan, and butter or olive oil. Stir until the spinach wilts and the soup looks creamy and cohesive.
Taste and adjust seasoning with more salt and pepper if needed.
Serve: Ladle into bowls and garnish with extra Parmesan and parsley. Serve with crusty bread if you like.