Whisk the eggs, salt and pepper together in a bowl.

Melt the butter with the oil in a 10" nonstick skillet over medium heat. Swirl to coat.

Add the eggs and cook, stirring gently in a circular motion until the mixture is thickened slightly. About a minute.

Use a rubber spatula to pull the cooked edges of the egg towards the center of the pan, tilting the pan so the uncooked egg runs to the cleared edge of the pan. Do this for about 30 seconds to a minute.

Cover the skillet in cook on the lowest heat for about five minutes.

Remove the pan from the heat and sprinkle most of the grated cheese on top. Cover with the lid and allow the cheese to melt for about 30 seconds to  minute.

Uncover and run the spatula around the outside of the omelette.

Slide half of the omelette onto the warmed dish using the spatula, then tilt the skillet so the remaining half flips over onto itself to form a half-moon shape.

Serve!