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 corned beef and the 1 beaten egg, green onion, salt and white pepper and mix to combine. Spread the bread crumbs on the bottom of a wide plate. With cold-water dampened hands, shape the potato mixture into four, 1" thick cakes. Set the cakes on the bread crumbs, turn to coat and gently press the crumbs on to help them adhere. Put water on to simmer to poach the eggs. Heat the oil in a large non-stick skillet set over medium heat. Cook the corned beef hash cakes 3 to 4 minutes per side, or until golden and heated through. Poach the eggs in the simmering water to the desired doneness. Plate the hash cakes, top each with a poached egg and serve.