Meanwhile, chop together finely the onion, prosciutto fat, garlic, celery, and parsley leaves. Place everything in a saucepan and cook over medium heat for about 5 minutes. When the onion and the fat are translucent, add the tomatoes, season generously with salt and pepper, and continue cooking for 20 minutes longer.
When the beans are tender, discard the bone, add the tomato sauce, and bring back to a boil. Add the pasta and cook until al dente. Let rest for a few minutes before serving.
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