Trim each artichoke of its outer leaves and choke.
Stuffing and cooking the artichokes
Mince the garlic, parsley and mint into a rough paste, season with salt and pepper. Fill the hallowed out cores of the artichokes with this mixture, packing it in well,
Then stand the artichokes up, stems upward, in a terracotta casserole or enameled cast iron Dutch oven or other heavy pot with tall sides.
NB: You may need to trim off a bit more of the stem so you can cover the pot tightly.
Pour a generous amount of olive oil over the artichokes, then pour enough water into the pot to come halfway up the artichokes (not counting their stems).
Season the artichokes generously. If you have any extra garlic-and-herb stuffing, you can add it to the cooking liquid.
Cover the pot tightly. Let the artichokes braise over medium-low heat for about 20-30 minutes, depending on the size and age of the vegetable.
Uncover the pot and allow the artichokes to cool before serving, moistened with a bit of the liquid.