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Put the potatoes in a large pan of salted cold water and boil for 6-8 mins or until tender. Drain well, return to the pan and shake with the lid on to fluff up the edges. Take care not to break up the chips too much.
Heat the oil in your largest saucepan to about 150C, when a little piece of potato should just start to sizzle. Fry the chips for 5-8 mins until crisp but not brown. Dry thoroughly on kitchen paper and leave to cool.
In a large bowl, mix together the beef mince, shallots, mustard, egg yolk and breadcrumbs until well combined. Divide into 4 equal portions and shape into burgers. Cover and chill the burgers in the fridge for at least 30 mins (you can prep these up to 2 days ahead).
Heat a griddle pan until hot and coat the burgers in oil. Cook for about 10-12 mins, turning regularly, until cooked through. Leave to rest on a plate under some foil. Cook the bacon in the pan until really crisp, then set aside with the burgers. Place the cut side of the buns onto the griddle to toast slightly.
Reheat the oil so that it’s really hot – about 180C – and again cook the chips for 5 mins or so until golden. Drain and sprinkle over sea salt. Spread ketchup over the toasted buns and fill each with the burgers and other ingredients. Serve with the chips and some coleslaw, if you like.