Heat the butter in a non-stick skillet over medium heat.
Add the sliced mushrooms and sauté until they are golden brown and tender, about 5 minutes. Season with salt and black pepper.
In a bowl, whisk the eggs until well beaten. Season with salt and black pepper.
Pour the beaten eggs into the skillet with the mushrooms. Cook for 2-3 minutes, or until the edges start to set.
Sprinkle the shredded Swiss cheese evenly over the omelette.
Using a spatula, carefully fold one side of the omelette over the cheese to create a half-moon shape. Cook for another 1-2 minutes, or until the cheese is melted.
Slide the omelette onto a plate and garnish with fresh parsley.