Heat the olive oil in a large pot or Dutch oven over medium heat. Add the chicken pieces and cook until lightly browned on all sides, about 5 minutes. You do not need to cook them through.
Add the chopped onion, carrots, and celery to the pot. Cook until the vegetables begin to soften, about 5 to 7 minutes.
Stir in the minced garlic and cook for 1 minute until fragrant.
Pour in the chicken broth. Add the Italian seasoning, thyme, salt, and pepper. Bring the mixture to a simmer.
Add the diced tomatoes (with their liquid) to the pot. Reduce the heat to low, cover, and let it simmer for 10 minutes, allowing the chicken to cook completely.
Increase the heat to medium-low. Add the refrigerated tortellini to the soup. Cook according to package directions, usually about 3 to 5 minutes, until the tortellini float.
Reduce the heat to the lowest setting. Stir in the heavy cream until fully combined. Do not let the soup boil after adding the cream.
Stir in the fresh spinach until it wilts, about 1 minute.
Remove the pot from the heat. Stir in the grated Parmesan cheese until melted and smooth. Taste and adjust salt and pepper if needed.
Serve hot.
Notes
For a Tuscan flavor variation, add 1/2 teaspoon of sun-dried tomato paste when you add the broth.
If you prefer a thicker soup, mix 1 tablespoon of cornstarch with 2 tablespoons of cold water and stir this slurry into the simmering soup before adding the cream.
You can substitute frozen tortellini, but you may need to increase the simmer time slightly.