Heat the olive oil in a large pot or Dutch oven over medium heat. Add the chicken pieces and cook until browned on all sides, about 5 to 7 minutes. Remove the chicken and set it aside.
Add the onion, carrots, and celery to the pot. Cook until the vegetables soften, about 5 minutes.
Stir in the minced garlic, Italian seasoning, salt, and pepper. Cook for 1 minute until fragrant.
Pour in the chicken broth and add the diced tomatoes. Bring the mixture to a simmer.
Return the browned chicken to the pot. Reduce the heat to low, cover, and simmer for 10 minutes, or until the chicken is cooked through.
Stir in the cubed cream cheese until it melts completely into the broth, creating a creamy base.
Stir in the heavy cream. Increase the heat slightly to maintain a gentle simmer.
Add the refrigerated tortellini and cook according to package directions, usually 3 to 5 minutes.
Stir in the fresh spinach until it wilts.
Remove the pot from the heat and stir in the grated Parmesan cheese just before serving.
Notes
For a pesto variation, stir in 2 tablespoons of basil pesto along with the heavy cream.
If you prefer a thicker soup, dissolve 1 tablespoon of cornstarch in 2 tablespoons of cold water and stir it into the simmering broth before adding the cream cheese.
You can substitute frozen tortellini, but adjust the cooking time as needed.