To make the pesto combine, garlic, pine nuts, and olive oil in a food processor. Puree until a rough paste form then add basil, lemon zest, and parmesan. Puree until the smooth, season to taste with salt and pepper. Just before serving stir in the lemon juice.
To cook the fish, heat the olive oil in a non-stick heavy based frying pan. Lightly season the Hoki fillet with sea salt, then pan-fry presentation side down, for 3-4 minutes or until ¾ of the way through. Turn-over and cook for another minute, add the butter and lemon juice then baste the Hoki with the pan juices. Remove from the heat.
To serve – place the Hoki fillets on to serving plates. Spoon over the lemon and basil pesto and serve.