In a stockpot, melt butter over medium heat. Add garlic, celery, and onion to pot and cook until onion and celery are translucent, about 3-5 minutes.
Whisk in flour and cook for another minute, stirring constantly.
Add half and half to half to pot and whisk with flour and vegetables. Allow sauce to simmer until it begins to thicken, another 3-5 minutes.
Pour chicken broth in the pot, whisking again until combined. Allow sauce to simmer again until desired thickness is reached. If you'd like a thinner soup, move on to the next step as soon as soon as the sauce seems thoroughly combined and has the consistency of heavy cream. If you'd like a thicker soup, continue to cook and stir for an additional 5-10 minutes.
Add salt, thyme, parsley, carrots, spinach, chopped chicken, and gnocchi to soup. Allow soup to simmer until heated through and gnocchi are soft, another 2-5 minutes.
Taste test soup for seasoning and add more salt if desired. Serve immediately with more fresh parsley for garnish.
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