In a large pot, heat the olive oil over medium heat. Add the celery, onions, and carrots, and sauté for 2-3 minutes until the onions become translucent.
Add the garlic and cook for about 30 seconds, just until fragrant, being careful not to let it brown.
Add the chicken, chicken broth, salt, pepper, and thyme. Bring the mixture to a boil, then gently stir in the gnocchi. Continue boiling for 3-4 minutes before reducing the heat to a simmer. Let it cook for another 10 minutes.
Stir in the half-and-half, heavy cream, and spinach. Cook for 1-2 minutes, or until the spinach wilts and becomes tender.
Taste the soup and adjust the seasoning with more salt and pepper, if necessary.