Heat the olive oil in a large soup pot over medium heat. Add the diced onion and cook for 3–4 minutes until softened. Stir in the garlic and cook for another 30 seconds.
Add the chicken breasts, crushed tomatoes, chicken broth, Italian seasoning, basil, salt, and black pepper. Bring to a gentle boil, then reduce the heat and simmer for about 15–20 minutes, or until the chicken reaches 165 degrees F internally.
Remove the cooked chicken from the pot and shred it with two forks. Return the shredded chicken to the soup.
Stir in the uncooked pasta. Simmer according to the package directions until tender, usually 8–12 minutes. Stir occasionally to prevent sticking.
Stir in the grated Parmesan cheese until combined. Ladle the soup into six bowls and divide the shredded mozzarella evenly among them. Garnish with basil or parsley if desired.