Zest the lemon into a small bowl and add the garlic, parsley, mint, olive oil, salt and pepper. Fill a large bowl with ice and water and squeeze the juice of the lemon into the water. Cut off the top 1 inch of the artichoke. Remove the outer leaves until you get to the tenderest yellow leaves. Cut the stems to within 2 inches of the base of the choke. Use a vegetable peeler or a sharp knife to remove the dark bark from the remaining stem. Using your fingers gently pry the leaves apart to reveal the inner choke. Use a small spoon or a melon baller to scoop out the small prickly leaves, with the purple edges and the fuzzy choke and discard. Place the prepared artichokes in the lemon water as you finish each to keep them from discoloring.
After all the artichokes are prepped remove them from the water. Spread the leaves and spoon about 2 tablespoons of the herb oil into each hollowed out center of the chokes. Close up the leaves as tightly as possible. Place the filled chokes, head side down, into a straight sided saucepot that is just big enough to hold all the chokes. Pack them in as tightly as possible so that they hold each other straight up during cooking. Pour water into the pot and fill it half full. Cover and cook over medium heat for about 50 minutes or until most of the water has cooked off. The artichokes can be served either hot or cold.
Stuffed artichokes are also a popular way to enjoy this Roman favorite.