Preheat the deep-fryer to 180°C and the oven to 210°C.
Boil three chopped parsnips in water and milk seasoned with salt and sugar.
Simmer for 12 minutes until the parsnips are tender.
Drain the parsnips and blend them into a purée using a food processor.
Transfer the purée to a pan and stir in cream until smooth.
Peel long strips from the remaining parsnip.
Fry the parsnip strips until golden, drain, and season with salt.
Boil red wine and chopped shallots in a small saucepan.
Simmer until the liquid reduces by half, add pepper, and cool.
Season the tuna and sear in a frying pan with olive oil.
Roast the tuna on a rack in the oven for 3 minutes.
Flip the tuna and let it rest in a warm place for 5 minutes.
Table each steak diagonally and return to the oven for 30 seconds.
Plate the purée, top with tuna, drizzle with sauce, and garnish with parsnip chips.