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Heat the oil in a large frying pan and cook the potatoes over a low heat for 10-15 minutes, turning occasionally.
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Add the garlic and bacon and increase the heat. Fry for 5-6 minutes, tossing occasionally, until the potatoes and bacon are golden.
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Add the onions and cook for 1 minute.
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Stir in the mustard and plenty of salt and pepper. Divide between four plates and keep warm.
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Half fill a small frying pan with water and bring to a simmer. Carefully break in the eggs and allow the water to come back to the boil. Simmer for 1 minute, then remove each egg using a slotted spoon.
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Top each plate of hash with a poached egg, sprinkle with black pepper and serve immediately.