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 hot water to cover all of the vegetables: the water should 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.