Heat the olive oil in a large skillet over medium-high heat. Add the potatoes, sprinkle with salt and pepper and saute until golden brown, 10 to 12 minutes.
Add the onions and peppers and continue cooking an additional 5 minutes. Add the cabbage and Worcestershire sauce and saute until the vegetables are tender, about 3 minutes longer. Stir in the corned beef and cream and reduce the heat to medium-low.
Crack the eggs over the hash. Cover with a lid and cook until the eggs are set, 8 to 10 minutes. Serve the hash divided among 4 plates.