This soup is even better the next day, so if you are a make-ahead kind of gal, this is perfect! Just cook the noodles the day you plan to eat it.
Chop the onion, garlic, celery and carrots. Heat olive oil in a large soup pot over medium high heat. Add chopped vegetables and cook until softened (about 5 minutes).
Add ground beef, salt, pepper, basil, oregano, rosemary, and red pepper flakes and stir to break up. Brown beef but do not overcook.
Stir in tomatoes, broth, parmesan rind and both cans of beans. Cover and bring to a simmer and cook on low for 20 minutes. Taste the soup to make sure carrots and celery are soft (if not cook an additional 10 minutes). Also, this is the time to add more salt if needed. If you are on the fence about if it needs more salt, add just a pinch, because the pasta you are adding next will need it.
Stir in the ditalini*. Cover and simmer 10 minutes or until pasta is al dente. Remove from the heat. Fish out the parmesan rind and discard. Serve the Pasta e Fagioli with grated Parmesan.
*Do not add the noodles until you are quite ready to eat. The longer they sit in the soup, the mushier and more bloated they become.
If you want to freeze this, I recommend cooking and freezing the ditalini separately.