In a mixing bowl, gently beat the eggs together with a pinch of salt and pepper.
Heat the olive oil and butter together in an omelette pan (or non-stick frying pan) until the butter begins to foam. Pour in the egg mixture and cook for a few seconds, allowing the omelette to set lightly before stirring the set part around the edges inwards. Repeat this motion 4-5 times, or until the omelette has lightly cooked through but is still soft and creamy in the centre.
Sprinkle the chopped smoked salmon into the middle of the omelette and fold the sides of the omelette inwards towards the centre. Turn the omelette out onto a serving, brush the omelette with butter and serve.
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