Place a large soup pot over medium heat and add 2 tablespoons olive oil.
Add 1 small white onion (finely diced), 1 stalk celery (chopped), 4 cloves garlic (minced), and 1 medium carrot (shredded). Sauté, stirring occasionally, about 3–4 minutes until the onion is translucent and the vegetables are softened.
Add the cooked, diced chicken (3–4 boneless skinless breasts or thighs), 5 cups chicken broth, 1 teaspoon salt, 1/2 teaspoon ground black pepper, 1/2 teaspoon dried basil, and 1/2 teaspoon dried thyme. Increase heat to bring the mixture to a gentle boil, then reduce heat and simmer uncovered for 10–15 minutes to meld the flavors.
Increase heat to return the soup to a gentle boil. Gently stir in 16 ounces potato gnocchi and cook 2–3 minutes, stirring occasionally, until the gnocchi float and are tender.
Reduce heat to low. Stir in 2 cups cream (or half and half) until warmed through but not boiling, then add 2 cups fresh spinach (roughly chopped). Cook 1–2 minutes more, until the spinach is wilted.
Taste and adjust seasoning with additional salt and pepper if desired. Serve hot.