Carefully wash and rinse all the vegetables; peel the potatoes, and remove the seeds from the tomatoes.
Cut them into small even pieces so that they cook evenly. Set aside the carrots, leek, and onion because they need a longer cooking time to release their flavor.
Put a little oil in a stockpot or dutch oven, brown carrots, leek, onion over medium-high heat for a few minutes (do not toast the onion and leek; otherwise, they will get bitter).
Add the other vegetables, the herbs, and the Parmigiano rind (if you choose).
Pour enough vegetable stock to cover all of the vegetables: the vegetable stock be about 1 inch (3 cm) above the vegetables.
Partially cover the pot with a lid and cook for about 25 minutes; add a little water if it gets too thick.
Before serving, remove the Parmigiano rind and season with little extra virgin olive oil.