In the same pot used to cook the chicken, under medium heat, melt the butter. Mix in the onions, celery, carrots and garlic. Cook until the veggies start to soften, 5-6 minutes. Mix in flour and cook while stirring for 1-2 minutes.
Slowly mix in the chicken broth to fully incorporate with the roux and veggies. Next, mix in the heavy cream and seasonings (dried parsley, oregano, thyme, salt and black pepper).
Continue cooking until the mixture reaches a simmer, then reduce heat to medium-low and simmer for 5-6 minutes.
Mix in the chicken and gnocchi and cook for 5-6 minutes while stirring intermittently to prevent the gnocchi from sticking to the bottom of the pot.
Mix in the Parmesan cheese and baby spinach. Continue to cook just until the spinach wilts. Remove from heat.
Spoon desired serving of the soup into a bowl. Grate over fresh Parmesan cheese (optional) and serve immediately on its own or with breadsticks.