Bring a large pot of heavily salted water to a boil over high heat. Add the package of tortellini and cook for 1 minute less than directed by the package directions. Drain the tortellini and set aside.
While the tortellini cooks, heat a Dutch oven or stockpot over medium heat. Add the olive oil and minced onions, carrots, and celery. Sauté, stirring regularly, for 8-10 minutes or until the onions turn translucent.
Add the minced garlic and chopped parsley. Cook for 1 minute, stirring regularly, until fragrant.
Stir in the tomato paste, cooking it for 1 minute.
Add the canned tomatoes, chicken broth, salt, and pepper. Stir well, increase the heat to high, and bring the mixture to a boil.
Reduce the heat to medium and simmer uncovered for 10 minutes, stirring occasionally.
Whisk the half-and-half and all-purpose flour together until a smooth slurry forms. Stir the slurry and the cubed cream cheese into the soup. Bring back to a simmer and cook for 5 minutes, stirring regularly, until the broth is smooth and most of the cream cheese chunks have dissolved (do not worry if they all haven’t; they will dissolve after the tortellini and chicken are added).
Stir in the cooked and drained tortellini, shredded rotisserie chicken, and chopped baby spinach. Simmer, stirring periodically, for 3-5 minutes until the spinach has wilted and the chicken is warmed through.
Season the soup to taste with additional salt and pepper. Serve hot, garnished with chopped parsley and grated Parmesan cheese.