For the duck hash, preheat the oven to 120C/250F/Gas ½.
Place the duck legs in a small roasting tray and cover with the duck fat. Cover the tray with aluminium foil and cook for 4 hours.
Drain and reserve the duck fat then leave the legs until cool enough to handle. Remove the duck meat from the bones and set aside. Reserve the duck skin.
Increase the oven to 170C/325F/Gas 3.
Bake the reserved duck skin in the oven for 4-5 minutes, or until crisp and golden-brown. Set aside to cool then break up into pieces.
Heat a little reserved duck fat in a frying pan and cook the onions for 5-10 minutes, or until caramelised. Remove the onions and set aside.
Heat a little more reserved duck fat in the frying pan and cook the duck livers for 3-4 minutes on each side. Drain the livers on kitchen paper, then chop and add to the duck leg meat.
Cook the diced potato in salted boiling water for 4-5 minutes, or until just cooked. Drain, then return to the pan and shake a little to roughen the edges. Set aside to cool.
Preheat a deep-fat fryer to 130C/265F (check using a digital thermometer). (CAUTION: Hot oil can be dangerous. Do not leave unattended).
Cook the potatoes in for 6-8 minutes, or until crisp, but pale. Set aside to drain on kitchen paper.
Increase the fryer to 180C/350F. Return the potatoes to the deep-fat fryer for 2-3 minutes, or until crisp and golden-brown. Set aside to drain on kitchen paper.
Heat two tablespoons of the reserved duck fat in the frying pan used to cook the onions and add the duck meat and cooked onions. Fry for 2-3 minutes, then add the fried potatoes and season with the Tabasco and Worcestershire sauce. Stir through the duck skin.
For the salad, place the pomegranate, celeriac, parsley and radish into a bowl.
Whisk the lemon juice and olive oil together until well combined.
Heat a little duck fat in a frying pan and fry the duck eggs until cooked to your liking.
To serve, dress the salad with the lemon dressing, a little truffle oil and sea salt.
Press the duck hash into a 9cm/3½in ring mould, then carefully remove the mould. Repeat on the remaining serving plates.
Using the same mould cut out each fried egg around the yolk and place on top of hash. Pile the salad alongside.