In a large pot, heat olive oil over medium heat. Add the diced chicken breast and cook for 5-7 minutes, until browned and cooked through. Remove chicken and set aside.
In the same pot, add the chopped onion and garlic, cooking for 2-3 minutes until softened and fragrant.
Stir in the diced tomatoes, chicken broth, heavy cream, basil, oregano, and salt and pepper. Bring to a boil, then reduce heat and simmer for 10 minutes.
Add the pasta and simmer for another 10 minutes, or until the pasta is tender.
Stir in the Parmesan and mozzarella cheese, letting it melt into the soup. Return the cooked chicken to the pot and mix.
Serve the soup in bowls, garnished with fresh parsley and extra Parmesan if desired.