Preheat your oven to 120°C.
Cover the duck legs with fat in a tray, seal with foil, and roast for 4 hours.
Shred the cooled duck meat from the bones and reserve the skin and fat.
Increase the oven temperature to 170°C.
Bake the duck skin for 5 minutes until crisp and break into pieces.
Caramelise the sliced onions in a pan with duck fat for 10 minutes.
Fry the livers for 4 minutes per side, then chop and mix with shredded duck.
Boil the diced potatoes for 5 minutes until just tender, then drain and shake to roughen.
Preheat a deep-fat fryer initially to 130°C.
Fry the potatoes for 8 minutes until crisp but pale and drain.
Increase the fryer to 180°C and fry potatoes again for 3 minutes until golden brown.
Combine duck meat, onions, and potatoes in a pan, seasoning with sauces and duck skin.
Toss pomegranate, celeriac, parsley, and radishes in a bowl.
Whisk lemon juice and olive oil together for the dressing.
Fry the duck eggs in a little duck fat until cooked to your preference.
Dress the salad with the lemon mixture, truffle oil, and sea salt.
Press the hash into 9cm ring moulds on serving plates.
Top each hash with a trimmed fried egg and serve with the salad.