Sharon fruit recipes. Sharon fruit is the trade name of a variety of persimmon grown in Israel. It is shaped like a tomato with thin, orange skin, a green stalk and orange flesh.It is a ‘non-astringent’ variety of persimmon but still has a tannic taste.haron fruit recipes. Sharon fruit is the trade name of a variety of persimmon grown in Israel. It is shaped like a tomato with thin, orange skin, a green stalk and orange flesh.