Add the butter to the dutch oven and heat, melting the butter. Add all the vegetables except the garlic and cook gently stirring to coat and saute until the vegetable, especially the carrot and celery are softened.
Add the minced garlic and saute for a further 30-60 seconds.
Add the flour and stir into the vegetable. Cook stirring constantly for about 1 minute to make a roux.
Add in the chicken broth, slowly at first stirring continuously to avoid making lumps and scrape up any bit on the bottom of the pot. Bring to a gentle boil.
Add the gnocchi and simmer uncovered for about 3 minutes until the gnocchi starts to float on the top.
Add the cooked chicken , chopped spinach, half and half and the parmesan cheese. Stir and heat until the spinach has wilted and the cheese has melted, about 3 minutes.
Season to taste and serve.