Heat olive oil in a large pot or dutch oven over medium heat.
Add celery, onions, garlic, and carrots and saute for 2-3 minutes until onions are translucent and vegetables are stating to become tender. .
Remove from pan, leaving any remaining oil, then add the gnocchi and 2 Tbs of butter, saute the gnocchi for 5 minutes, until browned and slightly crispy on the edges
Add celery, carrots, onion, garlic mixture back in to pot, if you are using the flour to have a slightly thicker soup, sprinkle flour over top, and stir it all togehter. Then add chicken broth, salt, pepper, and thyme, bring to a boil. Boil for 3-4 minutes.
Add cooked chicken in and reduce heat to a simmer and cook for 10 minutes.
Stir in half and half and spinach and cook until spinach is wilted and tender, about 1-2 minutes.
Taste, adjust seasoning by adding salt and pepper if needed, and serve.
Notes
You can replace the half and half with milk for a lower fat option or heavy cream if you want richer flavor.