Gently boil the potatoes in a generous amount of lightly salted water until tender. Drain well, thoroughly mash, and then transfer to a bowl; cool to room temperature. Add the cheese, egg, green onion, salt, white pepper and nutmeg and mix well to combine. Spread the bread crumbs on the bottom of a wide plate. With cold-water dampened hands, shape 1/4 cup amounts of the potato mixture into 1 inch thick cakes. Set the cakes on the bread crumbs, turn to coat and gently press the crumbs on to help them adhere. Heat the oil in a large non-stick skillet over medium heat. Cook the cakes 3 to 4 minutes per side, or until golden and heated through.
Note: 1 1/2 pounds of Yukon gold (yellow-fleshed) potatoes, peeled, halved and mashed, should yield about 3 cups of mashed potatoes. This information will be useful if you ever want to make these cakes with mashed potatoes you have leftover from another meal.
Options: Use russet or baking potatoes instead of Yukon gold potatoes. Instead of Swiss cheese, try a different tangy cheese in these cakes, such as Gouda or aged cheddar. Shape and coat the cakes in the breadcrumbs up to a day in advance; wrap and store in the fridge until ready to cook.