Prepare the pickled neeps. Peel and thinly slice the turnip. Meanwhile, bring the rest of the ingredients to the boil in a saucepan. Remove from the heat, drop in the turnip slices and leave to infuse for 2–3 hours.
Meanwhile, cook the haggis. Bring a large pot of water to the boil. Wrap the haggis in foil and lower into the pan. When the water comes back to a simmer, turn the heat right down and leave to cook slowly for 2–3 hours.
Once cooked, remove the haggis from the pan, unwrap and slice open. Take it out of the bladder and put into a large bowl. Let cool slightly, then mix in the egg yolks. Turn the haggis out onto a sheet of cling film and shape into a roll, about 5cm in diameter. Wrap in the cling film and refrigerate to firm up.
When ready, remove the pickled neeps from the liquid and cut into thin strips. Set aside.
Once chilled, unwrap the haggis and cut into 2.5cm slices. Put the flour, beaten egg and breadcrumbs into 3 separate containers. Dip the haggis slices first in the flour to coat, then into the beaten egg, and finally into the breadcrumbs to coat all over; set aside.
For the tatties, peel the potato and cut into wafer-thin strips using a Japanese mandoline. Mix with a little clarified butter and salt. Heat a non-stick frying pan, add a quarter of the potato and shape gently into a 5cm circle. Fry gently until crispy, then carefully remove and keep warm while you cook the rest of the potato in the same way to make 4 crispy potato cakes.
To fry the haggis cakes, heat the oil in a deep-fryer or other suitable deep, heavy pan to 180°C. Lower the haggis cakes into the hot oil and fry for 3–4 minutes until golden. Meanwhile, pile the neep strips onto warm plates. Remove the haggis from the pan, drain on kitchen paper and salt lightly.
Add a little more oil to the frying pan and fry the quail’s eggs for a minute or until the whites have set but the yolks are soft.
Place the haggis cakes alongside the neeps and top with the quail’s eggs. Place the crispy potato on the side and serve at once.