Heat the oil in a large pot over medium-high heat. Add the pancetta and cook, stirring, until slightly crisp and the fat has rendered, about 1 minute. Reduce the heat to medium and add the garlic, carrots, celery and onions. Cover and cook, stirring occasionally, until the vegetables soften, about 12 minutes. Add the zucchini, cover and cook, stirring occasionally, about 3 minutes. Add the cabbage and cook, stirring, until wilted, about 3 minutes more. Stir in the tomatoes and broth and bring to a boil. Stir in the pasta; lower the heat to a simmer and cook until the pasta is tender, about 8 minutes.
Mash half the beans in a small bowl with a fork. Add the mashed and whole beans to the soup and cook, stirring, about 3 minutes. Remove the soup from the heat and stir in the herbs and cheese. Season with salt and pepper. Divide among warm soup bowls and sprinkle with the Parmesan. Serve immediately with more cheese at the table.
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