Crack the eggs into a bowl, add a pinch of salt and pepper, and whisk together.
Heat a 7-inch pan on medium heat and add the olive oil and butter.
Once the butter has melted, swirl it around the pan to coat the bottom.
Pour the eggs into the pan and let cook for 20 seconds.
Use a spatula to bring the eggs from the sides into the center of the pan, tilting the pan to fill any gaps.
After 30 seconds, sprinkle the grated cheddar cheese over the omelette.
Let the omelette cook on low heat for 40 seconds until the eggs are set but still soft.
Use a spatula to loosen the edges of the omelette and fold it in half.
Slide the omelette onto a plate and serve hot.
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