Heat the olive oil in a large, ovenproof frying pan over a high heat, add the mushrooms and fry until tender.
In a medium bowl, combine the beaten eggs, courgette, cheese, fried mushrooms and tarragon, if using.
Preheat the grill to medium. Melt the butter in the frying pan over a medium heat and pour in the egg mixture. Gently pull the mixture from the outside to the centre with a spatula, tipping the pan to allow the raw mixture to flow to the edge again. When it begins to set, stop stirring and leave to cook for a few mins.
To set the top of the omelette, place the pan under the preheated grill for 5-6 mins. Serve with a green salad.