Heat the oil in a large frying pan, add the mushrooms and pancetta or gammon and fry for 5 minutes, stirring frequently, until golden. Stir in the crème fraîche and thyme, then remove the mixture from the pan and keep hot.
Wash and dry the pan. Whisk the egg whites into stiff, moist-looking peaks.
Mix together the egg yolks and mustard and season to taste with salt and pepper. Fold the mixture into the egg whites.
Heat the butter in the frying pan, add the egg mixture and cook over a medium heat for 3–4 minutes until the underside is golden. Quickly transfer the pan to a preheated hot grill, making sure that the handle is away from the heat, and cook for 2–3 minutes until the top is brown and the centre still slightly soft.
Spoon the mushroom and pancetta mixture over the omelette and fold in half. Serve immediately with a mixed salad.