Peel and finely chop the onion and garlic. Trim and slice the leek. Chop the potatoes, carrots, celery, and zucchini into cubes. Pick and roughly chop the parsley leaves.
Heat the olive oil in a large sauce pan over a medium heat and sauté the onion, garlic, and leek for 5 minutes.
Add the other chopped ingredients, the bay leaves, green beans, and chopped tomatoes. Drain and add the tinned beans. Cover with water, season, and simmer until the vegetables are tender.
Add the pasta and simmer until cooked, adding water if the soup is too thick.
Peel and add the garlic to a pestle and mortar. Add the garlic leaves and some sea salt. Poudn until puréed. Grate in the Parmigiano-Reggiano and muddle the extra-virgin olive oil to make a paste.
Serve the soup hot, with a dollop of pistou on top.