Pour flour into a shallow bowl; beat egg in a separate bowl. Dredge artichoke hearts in flour and then coat with egg.

Heat vegetable oil in a skillet over medium heat; cook and stir artichoke hearts in the hot oil until browned, about 5 minutes. Transfer cooked artichoke hearts to a bowl.

Pour oil out of skillet and wipe clean with a paper towel; return to stove top. Heat butter in the skillet over medium heat; pour in lemon juice. Return artichoke hearts to skillet and sprinkle with Parmesan cheese; pour in sherry. Season with salt and pepper; stir well.

Remove artichoke hearts from skillet using a slotted spoon and transfer to a serving dish. Boil sauce until reduced, 2 to 3 minutes. Pour over artichoke hearts; garnish with parsley.