Cool artichokes slightly. Spread leaves apart; pull out center leaves, and scrape out fuzzy thistle center (choke) with a spoon. Discard. After choke has been completely removed, scrape the artichoke heart with a spoon to remove as much pulp as possible; reserve pulp. (Be careful not to separate outer leaves from base of artichoke.) Set artichokes aside.
Finely chop reserved pulp; combine with mayonnaise and chopped egg, mixing well. Spoon mixture into center of each artichoke; chill. Place stuffed artichokes upright on lettuce leaves before serving.