Place the grapes and sugar in the bowl of a food processor and finely chop, using one-second pulses. Transfer the chopped grapes to a deep, medium skillet or a wide saucepan; stir in the lemon peel, salt, and water, and bring to a boil over medium-high heat. Cover the pan with a lid, reduce the heat to medium low and simmer for 18 minutes, until the fruit is very tender.

In a small bowl, stir the lemon juice and cornstarch together, and then stir into the grape mixture with the butter; simmer for 6 minutes or until desired consistency. Stir in the vinegar if using. Serve warm or cool.

Make ahead: Store cooled jam in a covered glass jar in the refrigerator for up to 2 weeks.