Heat olive oil in a large pot or Dutch oven over medium heat. Add celery, onion, and carrots. Cook for 3–4 minutes, stirring often, until fragrant and softened then add the garlic until fragrant about 1-2 minutes.
Pour in chicken broth, thyme, salt, and pepper. Stir and bring to a boil
Stir in the cooked, diced chicken and gnocchi and let boil for 3-4 minutes then reduce to a simmer for 10 more minutes so the flavors deepen.
Stir in the half and half and spinach. Let the soup gently simmer for another 3–4 minutes.
Taste and adjust seasoning with salt and pepper.
Ladle into bowls and top with cracked black pepper, a sprinkle of Parmesan, or a drizzle of olive oil. Serve with warm, crusty bread.