Chop the lemon zest and combine it with the olive oil.
Using a long knife, remove the skin from the salmon, remove any bones and cut it into 10 x 2 cm (4 x ¾ inch) strips. Stuff each olive with a piece of anchovy. Roll each olive in a basil leaf, wrap it in a strip of salmon. Skewer with a toothpick or small bamboo skewer to hold it in place. Sear the skewers for 5 mi