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Heat oven to 200C/180C fan/gas 6. Cut the potatoes into chunky chips, place in a pan of salted water and bring to the boil. Simmer for 5 mins until softened slightly, then drain and leave to steam-dry for a few mins.
Pour 3 tbsp of the oil into a shallow baking tray and place in the oven to heat for 5 mins. Meanwhile, toss the chips with the paprika, cayenne pepper and some salt. Carefully tip the chips into the hot oil and return the tray to the oven to cook for 40 mins, tossing them halfway through cooking.
Ten mins before the chips are ready, heat a large griddle pan. Cook the ham slices for 3 mins each side until they are hot and have griddle lines on both sides. Transfer to a plate to keep warm. In a small frying pan, heat the remaining oil and fry the eggs to your liking. Top each slice of ham with an egg and serve with the oven chips, and ketchup if you like.