Bring a large pot of salted water to a boil over high heat. Add the pasta and cook according to package directions until al dente. Drain and transfer the pasta to a baking sheet. Toss the pasta with a little olive oil to prevent sticking.
In a large saucepan over medium heat, warm the chicken stock.
In another large saucepan over high heat, heat 1/4 cup oil. When the oil is hot but not smoking, add the pancetta and cook until it begins to brown, 3 to 4 minutes, turning occasionally. Add the garlic and cook until it begins to brown, about 1 minute, stirring occasionally. Lower the heat to medium and add the onions, celery, and carrots.
Cook until the vegetables are soft, 8 to 10 minutes, stirring occasionally to prevent browning. Add the chopped herbs. Raise the heat to high. Add the beans, tomatoes, zucchini, and potatoes. Add the chicken stock and bring to a boil. Then bring it down to a simmer and cook until the potatoes are tender, 12 to 15 minutes, skimming any foam off the top of the soup. Season generously with pepper. Add salt, to taste. Just a few minutes before serving, add the cooked tubetti pasta. Serve warm with Parmesan and olive oil passed at the table.
Cooking notes: Add the cooked pasta just before serving. If it sits in the soup too long, it develops a flabby texture. Tubetti (little hollow tubes) are the classic pasta for minestrone, but you could substitute another small shape of pasta.