Heat the olive oil in a large pot over medium heat.
Add the onion, celery, and carrots. Cook for about 5 minutes until softened.
Stir in the garlic and cook for 1 minute until fragrant.
Pour in the chicken broth. Add the chicken breasts, Italian seasoning, oregano, basil, salt, and pepper. Bring to a gentle boil, then reduce heat and simmer for 15–20 minutes or until chicken is cooked through.
Remove the chicken and shred using two forks.
Return the broth to a boil and add the cheese tortellini. Cook according to package directions until tender.
Return the shredded chicken to the pot. Stir in the spinach until wilted. Add heavy cream and Parmesan if using.
Taste and adjust seasoning. Ladle into bowls and garnish with parsley and extra Parmesan.