Heat the olive oil in a large pot or Dutch oven over medium heat.
Brown the sausage.
Add the onion, celery, carrots, salt, and several grinds of pepper and cook, stirring occasionally, for 10 to 15 minutes, or until very soft.
Add the garlic, tomato paste, and rosemary and cook, stirring, for 1 minute.
Add the tomatoes and their juices, the beans, and the broth. Simmer for 20 minutes.
Add the pasta and simmer for 10 more minutes, or until al dente.
Stir in the spinach and red pepper flakes and cook until the spinach is wilted.
Season to taste and serve.
