Heat olive oil in a large Dutch oven or stockpot over medium heat.
Add carrots, celery, and onion; sauté for 5 to 7 minutes until vegetables are softened.
Stir in minced garlic and cook for 60 seconds until fragrant.
Pour in the chicken broth and season with oregano, basil, salt, and black pepper.
Bring the liquid to a rolling boil, then reduce heat to maintain a simmer.
Add the refrigerated tortellini and cook according to package instructions, typically 5 to 7 minutes.
Stir in the shredded chicken and baby spinach; cook for 2 minutes until the spinach is wilted and chicken is heated through.
Garnish with grated Parmesan cheese before serving immediately.