Pour a thin layer of the olive oil into a pan just large enough to hold the pieces of halibat side by side. Season the fish on both sides with a little salt, put it in the pan and pour over the rest of the oil - it should just cover the fish.
Very slowly heat the oil to 55-60ºC (130-140ºF), agitating it with a fish slice now and then so that it heats evenly. If you don’t have a thermometer, the oil should just feel unpleasantly hot to your little finger.
Now take the pan off the heat and leave it somewhere warm on top of the stove for 15 minutes to poach gently in the oil. The temperature should remain at 55-60ºC (130-140ºF); if necessary, keep taking the pan on and off a low heat to maintain this temperature.
Shortly before the fish is ready, heat the extra virgin olive oil in a large frying pan. Add the cucumber slices and toss over a medium heat for 1 minute. Add the dill, vinegar and a little salt.
To serve, divide the cucumber between 4 serving plates. Carefully lift the fish out of the oil, allowing the excess to drain off, and pput it on top of the cucumber. Pour the oil off into a jug, leaving behind the juices from the fish, which will have settled at the bottom of the pan. Spoon these juices around the edge of each palte, sprinkle the fish with a few sea-salt flakes and garnish with a sprig of fresh dill. Serve with some boiled new patatoes.
• 600ml (1 pint) olive oil
• 4 x 175g (6oz) pieces of thick halibut fillet, skinned
• 1 tbsp extra virgin olive oil
• 1 large cucumber, peeled & thinly sliced
• 1 tbsp chopped dill, plus a few sprigs to garnish
• 2 tsps white wine vinegar
• sea salt