If using dried beans, cover them completely with water in a pot and soak overnight.
Drain water the next day and rinse thoroughly.
In a large, heavy 4 - 5 quart pot, saute the "soffrito" of onion, carrots, and celery in the olive oil.
Add the parsley and garlic and saute for one more minute.
Fill the pot with the water and/or broth.
Add the tomato paste/ tomatoes and bring to a boil.
Add the chunk of parmigiana cheese.
Add the beans, reduce the heat just slightly and cook until slightly tender.
In a separate pot, boil the pasta for only a few minutes; you will continue to cook them for a few more minutes in the finished broth.
Bring the broth to a boil and add the semi-cooked pasta noodles and cook until al dente, about 5 minutes max.
Remove the soup from the heat and season with salt and pepper to taste.
Let stand 5 minutes.
Serve in warmed bowls.
Sprinkle with grated cheese.
Serve with freshly, grated Parmigiano cheese and fresh, crusty Italian bread.
THIS SOUP IS BETTER IF allowed to rest for 2 hours before serving; it thickens up nicely.
It is even better the NEXT day when all of the flavors are allowed to marry and blend!
If you choose to do this, boil the pasta in a separate pot for only a few minutes because it will continue to cook in the broth. Have the broth warming in another pot. Put the partially cooked pasta in the re-warmed broth and continue to cook until your pasta is al dente.
If you have the pasta noodles in for a long time, they become very large from absorbing the soup liquid, as well as become very soft and mushy.