Preheat a griddle pan. Cut the asparagus in half lengthways, toss in the olive oil and seasoning to taste. Lay the asparagus on the hot griddle pan and cook for 4-5mins, turning once until the asparagus is charred and tender. Beat the eggs with seasoning.
Melt a quarter of the butter in an medium frying pan. When sizzling, pour in a quarter of the egg mixture and cook for 3-4 mins, pushing the cooked egg into the centre of the pan with a spatula until no runny egg remains. Cook for 1 min until base is golden.
Scatter a quarter of the asparagus and salmon over the omelette and fold on to a plate. Sprinkle over the cheese. Repeat to make a further three omelettes in the same way.