Preheat the grill to high. Brush potatoes and scallions with olive oil and place on grill. Grill potatoes for 3 to 4 minutes on each side, or till just tender. Grill scallions until softened and you can see the grill marks. Remove scallions from the grill and cut into thin slices.
In a large bowl, whisk together 1/2 cup olive oil, Dijon mustard, apple and balsamic vinegars, and honey. Season with salt and pepper, to taste. Add potatoes, scallions, and parsley and toss until potatoes are well coated.