Boil potatoes in lightly salted water until tender. Drain well, mash, and transfer to a bowl to cool to room temperature. Fork-beat 1 egg and mix into potatoes, along with corned beef, green onion, salt and pepper.
Spread breadcrumbs onto a wide plate. Dip hands in cold water and shape potato mixture into four 1-in./2.5-cm thick hash cakes. Place on breadcrumbs, turn to coat and gently press crumbs onto hash cakes to stick. Set aside.
In saucepan, bring water to a simmer to poach remaining eggs. Meanwhile, heat the oil in large non-stick skillet on medium heat. Cook hash cakes 3 to 4 min. per side, or until golden and heated through. As hash cakes finish cooking, poach eggs in the simmering water 3 to 4 min., or to desired doneness.
Plate hash cakes; top each with a poached egg to serve.
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