Heat the oil and 2 tablespoons butter in a frying pan over a medium heat. Add the potato to the pan and cook for 6-8 minutes, turning, until tender and golden brown. Remove and set aside in a large bowl.
Add the mushrooms to the pan and toss well in the pan juices for about 3-4 minutes, until tender. Add the garlic and cook for a further minute, then season. Remove from the pan and toss with the potatoes and most of the chives.
Put the egg whites into a large bowl and whisk until soft peaks form. Gently beat the egg yolks in a separate bowl, then fold into the egg whites until completely mixed.
Heat half the remaining butter in the pan over a high heat and, when melted, add half the eggs. Lower the heat and cook for 2-3 minutes, until the underside is just set and golden. Sprinkle 1 side with half the cheese and add half the potatoes and mushrooms. Flip over the other half of the omelet and remove from the heat.
Sprinkle the omelets with the remaining chives and serve.
