In a large pot, heat olive oil over medium heat and sauté onion and garlic until fragrant.
Add chicken broth, Italian seasoning, salt, and pepper. Bring to a boil.
Stir in the lasagna noodles and cook until tender, about 10 minutes.
Lower the heat and mix in heavy cream, shredded chicken, and spinach.
Cook for 5 minutes, stirring occasionally, until the spinach wilts.
Add mozzarella and Parmesan cheese. Stir until the cheese melts and the soup thickens slightly.
Serve hot with crusty bread or garlic toast.