Finely slice the leek and dice the mushrooms.
Heat the oil in a non-stick frying pan, add the mushrooms and leek slices, cover the pan, and gently sauté until soft over low heat.
Whisk the eggs with three pinches of salt.
Add the egg to the vegetables and let it spread out evenly. When half cooked, scatter the parsley all over and add the cheese slices on one half of the omelette.
Put the lid on and cook for about 5-7 minutes, until the cheese is about to melt and the egg has set.
Fold the omelette in half. Cook for another minute or so, then slide it onto a plate. Cut it into half and serve.