Grate the potatoes, with their skin into a large bowl. Peel and grate the parsnip; add to the potatoes. Toss the vegetables with the scallions, parsley and season with the salt and pepper, to taste.
Heat a large (12-inch) nonstick skillet over medium heat and brush the skillet with about half the oil. Add the potato mixture and form into an even cake by pressing lightly with a spatula. Cook, shaking the pan periodically to prevent sticking, until the hash browns are crisp and brown, about 10 minutes.
Remove the pan from the heat; place a flat plate over the top of the skillet. Carefully flip the pan so the potato cake goes onto the plate. Brush the skillet with the remaining olive oil and then side the hash browns back into the skillet. Cook until browned and crisp, about 10 minutes more. Slide out of the skillet onto a heated serving plate. Cut into wedges to serve.