1. Heat oil in a large pot over medium-high heat. Add pancetta and cook, stirring, until slightly crisp and fat has rendered, about 1 minute. Reduce heat to medium, add onion, carrots, celery, and garlic. Cover and cook, stirring occasionally, until vegetables soften, about 15 minutes. Add zucchini, cover, and cook, stirring occasionally, for 3 minutes. Add cabbage and cook, stirring, until wilted, about 3 minutes more. Stir in tomatoes and broth; bring to a boil. Stir in pasta, lower heat to a simmer, and cook until pasta is tender, about 10 minutes.
2. In a small bowl, mash half beans with a fork. Add mashed and whole beans to soup and cook, stirring, about 3 minutes. Remove soup from heat and stir in herbs and cheese. Season with salt and pepper, to taste. Divide among warm soup bowls and sprinkle with Parmesan. Serve immediately with more cheese at table.
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