Rinse and chop the green beans and soup vegetables.
Peel the onions and garlic and chop finely, then sweat in a pot in hot oil until glassy. Add the beans and vegetables and sauté together. Pour in the broth and season with salt and pepper. Bring to a boil, then reduce heat and simmer for about 20 minutes.
Add the pasta and the drained beans to soup 5 minutes before the end of the cooking time. Dice the tomatoes, stir into the soup and season to taste.
To serve, pour the minestrone in bowls. Serve sprinkled with some finely chopped basil and grated Parmesan.