Heat the oil in a large saucepan over medium heat. Saute the onion for 4 minutes until transparent. Add in the carrots and garlic and saute for an additional 4 minutes.
Stir in the vegetable broth, tomatoes, orzo, thyme, oregano and rosemary. Bring the soup to a boil and reduce heat to medium low and simmer for 10 minutes, stiring occasionally.
Mix in the spinach and cook for around 1 minute, or until the spinach is wilted. Season with more salt and pepper to taste, and mix in the crushed red pepper flakes.