Heat the oil in a large saucepan over medium heat. Add the chicken and cook for 3 to 4 minutes, stirring as needed, until no longer pink.
Add the garlic, basil, oregano, salt, thyme, and chili flakes and cook for 1 minute.
Add the tomatoes, roasted red peppers, and cream.
In a small bowl, whisk together the broth and cornstarch and stir into the saucepan.
Add the tortellini, increase the heat to medium-high, and bring to a simmer. Reduce the heat to medium-low, cover, and cook for 3 to 4 minutes, until tender.
Stir in the spinach, mozzarella, and Parmesan. Taste and serve.
