Heat the olive oil in a large soup pot or Dutch oven over medium heat. Add the sausage and cook, breaking it up, until browned and cooked through. If there is a lot of grease, drain off all but about 1 tablespoon.
Add the onion and carrots. Cook 5 to 6 minutes, until softened. Stir in the garlic, Italian seasoning, and red pepper flakes if using. Cook 30 seconds.
Stir in the tomato paste and cook 1 minute.
Pour in the chicken broth and diced tomatoes. Bring to a gentle boil, then reduce to a simmer. Cook 10 to 12 minutes, until the carrots are tender.
Add the tortellini and cook according to package directions, usually about 3 to 5 minutes.
Reduce the heat to low. Stir in the heavy cream, spinach, and Parmesan. Cook just until the spinach wilts and the Parmesan melts into the broth. Do not boil.
Season with salt and black pepper to taste. Serve hot with extra Parmesan on top.