For the parsnip purée and parsnip chips, heat the vegetable oil in a deep-fat fryer to 180C/355F (CAUTION: hot oil can be dangerous - do not leave unattended) and preheat the oven to 210C/410F/Gas 7.
Roughly chop three of the parsnips, place them in a saucepan and cover with the water and milk. Season with salt and sugar, to taste, and bring to the boil.
Reduce the heat and simmer for 10-12 minutes, or until tender.
Drain the parsnips well, then place in a food processor with a little of the cooking liquid and blend to a purée.
Place the parsnips into a clean saucepan and add enough cream to create a smooth creamy purée. Season with more salt and sugar, to taste.
Using a vegetable peeler, peel long strips along the length of the remaining parsnip.
Carefully place the parsnip shavings into the hot oil and fry until golden-brown. Remove the parsnips using a metal slotted spoon and drain on kitchen paper. Sprinkle lightly with salt.
For the shallot and black pepper sauce, place the red wine and shallots into a saucepan and bring to the boil.
Simmer for 3-4 minutes, until reduced by half, then add the black pepper and leave to cool.
For the tuna, season the tuna loin with salt and freshly ground black pepper, and heat the olive oil in a frying pan. Fry the tuna on both sides until lightly coloured.
Place the tuna onto a rack on a small roasting tray and transfer to the oven to cook for 2-3 minutes.
Remove the tuna from the oven, turn it over on the rack and leave in a warm place to continue heating through for about five minutes. Leave the oven on.
Slice each tuna steak in half diagonally at 45 degrees, turn each piece flesh side up on the rack and then place back in the oven for 30 seconds. Remove the tuna from the oven.
To serve, place a large spoon of parsnip purée in the middle of each of four plates and spread slightly. Arrange the tuna on top, flesh side up. Spoon over the shallot and black pepper sauce, and top with the fried parsnip.