In a non-stick frying pan, melt the butter with olive oil over medium low heat.
In a small bowl, beat the eggs vigorously with salt and pepper. Pour the eggs into the pan and move the pan to spread the eggs into a thin layer by twisting it around. Wait a couple minutes until the eggs begin to solidify at the middle of the pan.
Add desired fillings to the outer edge of half of the omelette. Flip half of the omelette onto itself using a spatula. Let it sit for a minute and serve.