Fill a bowl with water, squeeze in the juice from the lemon, add the lemon rind and stir.
Trim the artichokes by cutting off the top quarter of the head and removing the tough outer leaves. Trim the stems, leaving about 2-2¾ (5–7 cm) attached. Trim the outer layer of the stems and remove the centre, using a spoon to scoop out the hairy choke. Once cleaned, immediately place the artichokes in the lemon water to stop them turning brown.
Finely chop the mint and garlic, and season with salt and freshly ground black pepper. Drain the artichokes well and fill the centre of each artichoke with the mint mixture.
Stand the artichokes, stem side up, in a heavy-based saucepan wide enough to hold them all in one layer. Pour in the water or wine and drizzle with the olive oil.
Cover and cook over medium-low heat for about 1 hour, or until tender. Test if the artichokes are ready by pushing a toothpick into the base of the stem.
Serve warm, or at room temperature.