Heat a large soup pot on medium-high heat and add the oil.
Add the carrots, celery, and onion and cook until crisp-tender, about 4-5 minutes.
Add the sausage meat and cook until browned, about 4-5 minutes, stirring often.
Stir in the tomato paste, garlic, parsley, salt, oregano, basil, and red pepper flakes if using. Cook for 2 minutes.
Add the broth and tomatoes and bring to a boil. Stir in orzo, reduce heat to medium-low, cover, and simmer until pasta is al dente (8-10 minutes).
Stir in spinach and cream. Serve hot.
