Heat a large Dutch oven over medium/high heat. Add butter. When the butter is melted add the onion to the pot and sprinkle with ¼ teaspoon salt. Saute the onion for 3-4 minutes.
Add the celery and garlic to the pot, stir, and saute for an additional 3-4 minutes.
Next, add the chicken thighs (thigh side down) to the Dutch oven and brown the chicken for 1 minute.
Pour the chicken broth over all of the ingredients and add the remaining salt to the pot. Bring to a boil.
Turn heat to medium/low, cover, and let simmer for 10 minutes or until the chicken thighs are cooked.
Carefully remove the chicken thighs from the Dutch oven and shred with 2 forks. Set aside.
Add the spinach, carrots, and gnocchi to the pot and turn the heat back to medium/high and let the soup simmer until the gnocchi floats to the top of the soup. Turn heat to low.
Carefully remove 1 cup of hot broth from the pot and create a slurry by adding the flour to the 1 cup of hot broth. Whisk the two together until a thick slurry forms.
Use a spatula to scrape the slurry back into the pot and whisk the slurry into the soup. The soup should thicken quickly.
Add the chicken back into the soup and mix.
Remove the soup from the heat and slowly add the heavy cream to the pot. Mix until the cream is combined into the soup.
Add black pepper and stir.
Heat the soup to the desired temperature over low heat and enjoy.