Place 375g of tuna between two sheets of cling film and flatten with a rolling pin until very thin.
Remove the top film, place a 20cm plate over the tuna, and cut around it to form a circle.
Heat oil in a pan and fry the sourdough slices on both sides until crisp.
Remove the remaining film and lay the toasted bread over the thin tuna layer.
Flip the plates so the tuna carpaccio rests on top of the bread on a serving plate.
Dice the remaining tuna and mix in a bowl with shallot, mustard, lemon juice, and half the chives.
Garnish the carpaccio with the tuna tartare and the remaining chives.