This is the classic and authentic Italian minestrone with a green twist. No tomatoes here! You may brown some pancetta or bacon in olive oil before proceeding with the recipe if you wish. I prefer to use a good quality vegetable bouillon to vegetable broth. The taste is more authentic and you simply need to skip the salt.
Heat 2 tablespoons olive oil in a heavy-bottomed pot over medium-high heat; cook and stir onion and garlic until onion is translucent, about 10 minutes. Add green beans, peas, and zucchini; toss to coat vegetables with oil.
Slowly stream vegetable broth into vegetable mixture; bring to a simmer over medium heat. Stir in rosemary and great Northern beans and bring back to a simmer, about 5 minutes. Add ditalini pasta and simmer soup until pasta is tender but firm to the bite and soup has thickened, 10 to 15 minutes. Remove from heat; stir in parsley.
Ladle soup into serving bowls and top each serving with 1 heaping tablespoon Parmesan cheese; season with salt and black pepper. Garnish soup with a drizzle of extra-virgin olive oil.