Heat oil in a medium pot over medium heat until it reaches 350 on a deep-fry thermometer; when oil is hot, reduce heat to low.
Mix mayonnaise and sesame oil; set aside.
Use a paring knife to shave stem ends of the artichoke to a point like a pencil.
Remove all outer green and tough leaves until you reach the yellowish core.
Cut each artichoke in half and put in a bowl of ice water. Squeeze lemon quarters into water and drop in peels.
Drain artichoke pieces and blot dry with a towel. Working in 2 batches, cook artichokes until browned and crispy, about 8 minutes. Use a slotted spoon to transfer to a paper towel to drain.
