Boil the potatoes in a pan of salted water for five minutes, then drain.
Heat two tablespoons of the oil in a pan and fry the onion and garlic for 6-8 minutes, or until softened and lightly browned.
Tip the onion mixture into a bowl with the corned beef, Worcestershire sauce, chopped gherkin and mustard. Season with salt and freshly ground black pepper and mix well.
Transfer this mixture to an ovenproof dish.
Heat the remaining tablespoon of oil with the butter in a frying pan and fry the potatoes until tender and golden-brown.
Preheat the grill to high.
Spoon the potatoes on top of the meat mixture in the dish, then place under the grill for 4-6 minutes, or until crisp and golden-brown.
To serve, divide the corned beef hash among four serving plates. Top each portion with a poached egg and serve with brown sauce and tomato ketchup.
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