Using a very long thin knife, cut the fillet on a diagonal into wide thin slices, without breaking through the skin. The slices should look like thin slices of smoked salmon. Spread the slices out on chilled plates, without overlapping. Sprinkle with the juice of 1 lemon, salt and several good turns of the pepper mill.

Cut the basil leaves into fine julienne strips and scatter them over the salmon. Then let 3/4 tablespoons of the olive oil run over the surface of each portion. Tilt the plate from side to side until the entire surface of the salmon is coated.

This must not be done any earlier than 30 minutes before serving.