Heat olive oil in a large cooking pot over high heat.
Pat dry the chicken with paper towels. Season with salt and pepper.
Sear the chicken in the hot olive oil until deep golden all over. Don't stack the chicken in the pot if necessary, sear in two batches. Once done, remove the chicken from the pot and set it aside on a plate.
Turn the heat to medium-low. Add to the pot the leeks, onions, and garlic. Saute for a few minutes until caramelized, stirring and scraping the pot.
Pour the vinegar (or white wine) into the pot. Add the chicken back to the pot along with its juices that have collected on the plate.
Cook for a couple of minutes without stirring until the liquid in the pot drains and it stops smelling vinegary (or like alcohol if using wine). Don't stir at this point just tilt and shake the pot a little.
Pour in the stock season with salt, pepper, bay leaves, and thyme. Once it gets to a gentle boil, turn the heat to low and put the lid on. Simmer for 30 minutes.
Add the potatoes to the pot making sure they're submerged in the sauce. Add also the carrots, celery, and zucchini. Raise the heat to medium. Put the lid back on and simmer for 25-30 minutes more. Or until the potatoes are cooked.
Mix together the cornstarch with lemon juice and lemon zest. Pour it into the pot. Add also the butter.
Shake the pot a little. Raise the heat to high and cook uncovered for 2-3 minutes or until the sauce thickens nicely.
Serve with plenty of freshly ground pepper on top and enjoy!