In a large pot, heat olive oil over medium heat. Add the diced chicken and cook for 5-6 minutes, or until fully cooked. Remove and set aside.
In the same pot, add the onion, garlic, carrots, and celery. Sauté for 5-6 minutes, stirring occasionally, until the vegetables are softened.
Pour in the chicken broth and add the Italian seasoning. Stir to combine and bring to a simmer.
Return the cooked chicken to the pot and simmer for 10-15 minutes to meld the flavors.
Stir in the heavy cream, Parmesan cheese, and nutmeg (if using). Simmer for an additional 5 minutes, stirring until the soup is creamy.
Add the chopped spinach and cook for 2-3 minutes, or until wilted.
Season with salt and pepper to taste. Serve hot, garnished with fresh parsley if desired.