Trim the artichokes to their yellow portions, and using a grapefruit spoon, scoop out the hair chokes. Cut in half. In a large lidded pot, heat the oil until smoking. Carefully lower the artichokes into the oil, and cook, turning once, for approximately 5 minutes. Add the garlic, mint, parsley, and salt, then cover again, simmering for 5-6 minutes. Slowly pour in the wine, then lower the heat and cook for 20 minutes. The chokes should be fork tender when done.
Pour out the oil into a long thin platter with high sides. Line the artichokes in single file up the center and squeeze the lemon juice over them just prior to serving.