Preheat the grill to medium-high. Put the eggs in a large bowl, with seasoning, and whisk together.
Put the butter in an ovenproof frying pan and melt over a medium heat. Pour the egg into the pan and cook until set. Scatter over the mushrooms and chestnuts.
Transfer the pan to the grill. Cook for 2-3 minutes, then remove the pan and drizzle the omelette with olive oil. Sprinkle over the parsley, then fold the omelette and cut in half and divide between two plates to serve.