Microwave the cream cheese in 20-30 second intervals until very soft, making it easier to incorporate.
In a large soup pot, heat the olive oil and butter over medium-high heat. Add the chopped onion and sauté for 5 minutes until softened.
Add the minced garlic and cook for 30 seconds, then add the mushrooms and Italian seasoning. Cook for 5-6 minutes until the mushrooms have released their water and are tender.
Sprinkle the flour over the mixture and stir continuously for about a minute to cook off the raw flour taste.
Stir in 2 cups of the chicken broth, ensuring all the flour dissolves, then add the remaining 4 cups of broth.
Pour in the heavy cream and add the broken lasagna noodles. Increase the heat to high, bringing the soup to a boil. Once boiling, reduce to a gentle simmer. Stir occasionally to prevent the noodles from sticking, and cook with the lid slightly ajar for 20 minutes.
Add the shredded chicken and softened cream cheese (cut into smaller pieces). Increase the heat slightly to help the cream cheese melt, stirring continuously until fully incorporated, about 3-5 minutes.
Stir in the parmesan and fresh spinach, allowing the cheese to melt and the spinach to wilt. Season with salt and pepper to taste.
The soup should be creamy and slightly thick. If a thicker consistency is desired, let it simmer a bit longer; for a thinner soup, add more broth or cream as needed.