Heat grill to medium.
Toss the potatoes, onion, and 2 tablespoons of the oil in a bowl. Arrange in a single layer on the grill. Grill the potatoes and onion, turning frequently, until they are tender and slightly charred, about 15 minutes.
Transfer to a bowl. Add the parsley, vinegar, the remaining 2 tablespoons of oil, 1 1/4 teaspoons salt, and 1/4 teaspoon pepper and toss to coat.
Serve warm or at room temperature.