Heat the olive oil in a large pot or Dutch oven over medium heat. Add the diced onion, carrots, and celery. Sauté for about 5 to 7 minutes, or until the onions are translucent and the vegetables begin to soften. Add the minced garlic and cook for another 60 seconds until fragrant.
Add the bite-sized chicken pieces to the pot. Season with Italian seasoning, salt, and pepper. Cook the chicken for about 5 minutes, stirring occasionally, until the exterior is no longer pink. The chicken doesn’t need to be fully cooked through yet, as it will finish simmering in the broth.
Pour in the chicken broth and bring the mixture to a boil. Once boiling, reduce the heat to low and let it simmer for 10 minutes. This allows the flavors of the vegetables and herbs to meld with the broth and ensures the chicken is tender.
Turn the heat back up to medium-high to bring the soup to a gentle boil. Add the refrigerated cheese tortellini to the pot. Cook according to the package directions, usually about 3 to 5 minutes, until the pasta is tender and floats to the top.
Lower the heat to low. Stir in the fresh baby spinach and heavy cream. Stir gently for 1 to 2 minutes until the spinach has wilted and the soup is heated through. Taste and add more salt or pepper if needed.