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Make the tartar sauce: mix together all the ingredients and season to taste. Set aside.
Put the flour, egg and breadcrumbs on separate plates. Season the flour, then dip the strips of salmon in it to coat. Dust off any excess, then dip in the egg and finally roll in the breadcrumbs. Heat a grill to high and grill the fish fingers for 3-4 mins each side, or add the oil to a non-stick frying pan and cook for 3-4 mins each side.
Arrange the Little Gem leaves in the split sub rolls, then stuff each with a couple of fish fingers, followed by a good dollop of the tartar sauce.