In a nonstick pan, heat the oil over medium-high heat. Add the bell pepper, mushrooms, onion and garlic and cook, stirring, until lightly caramelized, about 4 minutes. Add the corned beef and potatoes and cook until the potatoes begin to crisp, about 5 minutes; try not to move the pan to allow the potatoes and meat to brown. Season with salt and pepper. Add the scallions and toss.
In a separate nonstick pan with some oil, cook the eggs sunny-side up or over easy, depending on your preference. A runny egg is best for this dish so it will be creamy when mixed with the hash.
Put the hash on a plate and top with the eggs. Garnish with additional scallions.