Prepare the Base: Heat olive oil in a large pot over medium heat. Add the chopped onion, carrots, and celery. Sauté until the vegetables are tender, about 5 minutes. Stir in the minced garlic and cook for an additional minute.
Add the Broth and Chicken: Pour in the chicken broth and bring it to a simmer. Add the cooked, shredded chicken and stir to combine.
Make It Creamy: Reduce the heat to low and stir in the heavy cream and milk. Season with Italian seasoning, salt, and black pepper. Let the soup simmer gently for 10 minutes.
Cook the Gnocchi: Add the potato gnocchi to the soup and cook according to the package instructions, usually about 3-5 minutes.
Add Spinach: Stir in the chopped spinach and let it wilt in the hot soup for about 2 minutes.
Serve and Enjoy: Ladle the soup into bowls and garnish with grated Parmesan cheese, if desired. Serve hot with crusty bread or a side salad.