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Bring a large pan of salted water to the boil. Add the potatoes and boil for 5 mins until just tender. Drain well and leave in the colander to steam-dry.
Meanwhile, spray an ovenproof pan with cooking spray. Add the leeks with a splash of water and fry until very soft and squishy. Add a few more sprays of the oil, tip in the potatoes along with the ham, and fry to crisp up a little. Heat oven to 200C/180C fan/gas 6.
Stir in the mustard, 1 egg and a good amount of seasoning with a fork – break up some of the potatoes roughly as you do. Flatten down the mixture, spray the top with oil, and bake in the oven for 15-20 mins until the top is crisp.
When the hash is nearly ready, heat 200ml water in a non-stick frying pan with a lid (or use a baking sheet as a lid). When it is steaming (but before it simmers), crack in the remaining 4 eggs and cover with a lid. Cook for 2-4 mins until the eggs are done to your liking. Meanwhile, heat the beans.
Lift an egg onto each plate, add a big scoop of hash and spoon on some beans.