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 and cook, turning frequently, until 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 to the potatoes and onion and toss to coat. Serve warm or at room temperature.