Begin by placing the potatoes in a large saucepan of water and bringing them to the boil. Simmer for 20 minutes or until the potatoes are tender. Strain the potatoes off the water, mash with 50g butter and season with salt and pepper. Leave aside to cool for 10 minutes and add the egg and the flour. Combine thoroughly and shape 4 -8 patties of 2 cm thickness.
Heat the oil in a pan over a medium to low heat, add the potatoes cakes and cook for 5-8 minutes until golden brown on both sides. Add some butter and baste the potatoes cake with the foaming butter. Keep warm in the pan until ready to serve.
Meanwhile, in a second sauté pan, over medium heat. Drizzle some oil and crack 4 eggs. Season with salt and pepper and slowly cook the fried eggs. Cook for 2-3 minutes then add some butter and let the butter foam. Baste the eggs until cooked to your liking. Using a lifter, remove and drain on a plate lined with paper towels.
To serve, transfer each potato cakes onto serving dishes and top with the fried egg.