Heat oil and butter in a 16cm (base) 20cm (top) non-stick frying pan over medium-high heat. Add mushrooms and cook for 5-6 minutes, turning occasionally until light golden and just tender.
Sprinkle over the nutmeg and turn to coat. Remove one-quarter of the mushrooms to a plate, cover to keep warm. Reduce heat to low.
Whisk the eggs, thyme and half the parmesan together until well combined then pour over the mushrooms. Gently shake the pan to allow egg to run to the base of the pan. Season with a little pepper and cook for 3 minutes.
Preheat grill to medium heat. Place the pan under the grill and cook for 3 minutes until omelette is light golden and cooked through. Top with reserved mushrooms, spinach and remaining parmesan. Serve with toasted bread.