Grate the potatoes on the largest hole of a box grater and add to a large bowl of cold water. Stir around until water looks cloudy. Drain in a colander, pressing out as mush water as possible, then wrap up in a clean linen towel and wring dry over the sink to expel excess water. Transfer dried potatoes to a dry mixing bowl and add scallions. Toss together and season generously with salt and pepper.

Heat half of the butter and oil in a heavy 10-inch (25 cm) skillet. Once hot, add the potato mixture, toss around to coat in the oil, then form one layer that fills the pan side to side and press down firmly. Cook over medium heat for at least 10 to 15 minutes or until golden brown on the bottom (you can peek to look). Use a large, sturdy spatula to flip potatoes over in 3 or 4 sections. If the pan looks dry (and it probably will), add the additional butter and oil. Don’t worry if the potatoes break up a bit. Just try to get all of the “top” of the potatoes now onto the bottom. Continue to cook over medium heat until well browned again, at least 10 minutes more. The potatoes should be cooked and tender with lots of crispy bits. Serve immediately.