Preheat grill. Brush potatoes and green onions with 1/4 cup of the olive oil. Grill the potatoes until tender, 4 minutes on each side. Cut the potatoes into 1-inch cubes and finely chop the green onions. (Do not grill the green onions.)

In a large bowl, whisk together the remaining 1/2 cup olive oil, mustard, vinegars, and honey and season with salt and pepper. Add the potatoes, green onions and parsley and mix until the potatoes are coated with the dressing. Season to taste with salt and pepper.