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