Fazool, Fagioli, will give you more options to search if you care to look on Google.
I think the difference between minestrone and fagioli is the vegetables. Minestrone has them and Fagioli does not. I find the fagioli to be more liquidy than a ministrone
And this is what I LOVE about cooking - put it on the table and no matter how it is I bet it's good!
A friend made her "secret" family recipe and it was VERY basic. What I had was a light red broth, tomatoes, white beans, pasta, and a bit of hamburger. I'm sure garlic was in there but for the life of me I don't remember onions, unless they were pulverized to where they did not show - and that goes for the carrots and celery because the broth was VERY flavorful - but those ingredients just weren't in the final product. She may have even cooked them in there and then removed them.
If you take busyfinger's recipe, use all dried herbs, add some chicken broth AND some tomato sauce but still have a light broth, you will be VERY close. And, some ground beef.
IMHO, fresh parsley is too "bright" for a pasta fagioli. This definitely requires dried herbs.
And the white/cannellini beans can certainly be changed to kidney beans or a combination thereof.