1. In a large pot (6 to 8 quarts), heat 1 tablespoon oil over medium heat. Add onion, leek, carrot, and garlic; cook, stirring frequently, until onion is translucent, 3 to 4 minutes. Stir in zucchini, cabbage, and rosemary; cook, stirring, until vegetables are coated, 1 to 2 minutes.

2. Add tomatoes and enough water (about 6 cups) to cover vegetables by 1 inch. Bring to a boil; reduce heat to a simmer. Season with salt and pepper. Cook until vegetables are tender and soup is thickened, about 10 minutes.

3. Stir in beans and pasta; cook until pasta is al dente, 10 to 15 minutes. Season with salt and pepper. Divide among bowls. Garnish with Parmesan, and drizzle with oil, as desired.