Remove the tough outer leaves of the artichokes. With a sharp knife trim off the tips of the leaves and the skin off the stem. Do not cut off the stem. Open the leaves and remove the beard from the center. Place the artichokes in cold water and lemon juice, to avoid discoloration.
Wash and chop finely the mint and garlic. Remove the artichokes from the water, open the leaves and fill the center with mint, garlic, salt and pepper.
Then place them upside down tight side by side (with the stem up) in a pot at least as tall as the artichokes. Salt and pepper to taste, sprinkle olive oil, add as much cold water as needed-to just cover the artichokes, cover and let cook over medium heat for about 1 hour.
Cool and place them in a deep dish and cover with the cooking juice (If there is too much liquid, first reduce over a high flame).
They are best served warm, but may also be served at room temperature.
Caution about seasoning liquid before cooking, if it is to be reduced laser, or it may be over salty