Cook the peeled, chopped potatoes in a saucepan of salted boiling water for 8-10 minutes, or until tender. Once tender, drain and set aside.
Meanwhile, heat one tablespoon of the olive oil in a large non-stick frying pan. Cook the onion with a pinch of salt over a medium heat for about five minutes, or until softened and turning golden-brown. Once the onions are cooked, push them to the edge of the pan.
Add a little more oil to the pan and then add the potatoes, crushing them roughly with the back of a fork. Spread them out so that they cover the base of the pan and leave to cook for 4-5 minutes, or until a golden crust is beginning to form on the base. Turn and repeat until all the sides of the potatoes are golden-brown. Mix with the onions at the edge of the pan.
Add the corned beef and English mustard to taste and stir through to mix well. Continue to cook over a low heat while you prepare the eggs.
Add the remaining olive oil to a separate frying pan. Once hot, crack in the eggs and fry until the white is cooked through, but the yolk still runny.
Serve the hash divided between serving plates with an egg on top and eat immediately.