In a bowl, beat together the eggs, milk or water, salt, pepper and green onion. Melt the butter in an 8-inch, non-stick skillet set over medium heat; pour in the eggs. As mixture sets at the edges, use a heatproof spatula to gently push the cooked portions towards the center of the pan. When the surface of the eggs are almost set but still look moist, top one half of the omelette with the cheese and smoked salmon. Fold the omelette in half and cook 1 minute more. Slide onto a warm plate and serve.