Begin by melting butter in a large pot set over medium heat.
Add the celery, carrots, onion, and garlic; cook and stir occasionally until the vegetables have softened, about 8 minutes.
Sprinkle in the flour and cook, stirring for about 2 minutes to remove the raw taste.
Gradually pour in the chicken broth while whisking to keep the mixture smooth and prevent lumps.
Stir in the cooked chicken and bring the soup to a full boil.
Add the gnocchi and simmer until they float and are tender, roughly 5 minutes or according to package directions.
Turn the heat down to medium-low and mix in the heavy cream. Warm gently until the soup is hot and steaming but does not boil.
Fold in the spinach, fresh thyme, salt, and pepper; cook just long enough for the spinach to wilt and all ingredients to meld together.