Grate the potatoes on the large holes of a box grater into a large bowl and toss with the scallions, cayenne, nutmeg, 1/2 teaspoon salt and a few grinds of pepper.
Heat 1 tablespoon of the oil in a large nonstick skillet over medium heat. Add the potato mixture and press into an even layer with a spatula. Cook, shaking the pan occasionally to prevent sticking, until the potatoes are crisp and brown on the bottom, about 10 minutes.
Remove the skillet from the heat and put a flat plate over it. Carefully flip the skillet so the potatoes fall onto the plate in one piece. Return the skillet to medium heat and add the remaining 1 tablespoon oil, slide the potatoes back into the skillet, browned side-up. Continue cooking until browned and crisp, about 10 minutes more. Slide the hash browns out of the skillet onto a cutting board and cut into wedges.
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