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Cut the potatoes into cubes and, in a large frying pan, fry them in butter for 15 mins until golden and cooked through.
Tip in chopped rosemary leaves, mushrooms and garlic and fry for a few mins until softened.
Season to taste, then push veg to the side of the pan and add a further 1tbsp oil. Break in the eggs and fry to your taste.
Serve the potatoes piled on two plates and top each serving with a fried egg.