Heat olive oil in a large pot and cook onion, carrots, celery, and garlic until soft and fragrant. This step builds the base flavor of the soup. Stir occasionally to prevent burning and ensure even cooking.
Add the cooked shredded chicken into the pot and mix well with the vegetables. Let it cook for a couple of minutes so it absorbs the flavors. This helps enhance the overall taste of the soup.
Add chicken broth, heavy cream, and cream cheese to the pot. Stir until the cream cheese melts and blends smoothly. Bring everything to a gentle boil, then reduce heat to simmer.
Let the soup simmer for about 15 minutes to develop rich flavors. Stir occasionally so nothing sticks to the bottom. This step helps create a creamy and well-balanced broth.
Stir in the pasta and shredded cheddar cheese. Let it cook until the pasta is tender and the cheese melts completely. The soup will start to thicken beautifully.
Add chopped spinach toward the end and cook until wilted. Season with salt and pepper to taste. Serve hot with parmesan on top if desired.