Preheat the oven to 400?F.
Place the potatoes in a large roasting pan and toss with 1/4 cup of the extra virgin olive oil. Season with 1/2 teaspoon salt and 1/2 teaspoon pepper. Wrap the garlic head in foil and add to the pan. Roast the potatoes and garlic until tender, 35 to 40 minutes. Remove from the oven and let stand until cool enough to handle.
Meanwhile, heat the olive oil in a large skillet over medium heat. Add the onions and cook until golden brown, about 10 minutes. Remove from the heat.
Once the garlic is cool enough to handle, squeeze as much pulp as possible from the head into the bowl of a food processor. Add the egg, green onions, lemon juice, rosemary, remaining 3/4 teaspoon salt, and remaining 1/2 teaspoon pepper. Puree until smooth. With the machine running, slowly add the remaining 1 cup extra virgin olive oil. The mixture will thicken.
Combine the potatoes and onions in a large bowl. Toss with 1 cup of the garlic dressing and the parsley. Serve immediately.
Makes 8 servings