Melt the butter in a medium frying pan over medium heat.
Pour in the beaten eggs. Stir and shake the pan, moving the eggs around until a few curds form. Reduce the heat to low, then flatten the eggs until the still-runny egg covers the entire bottom of the pan. Add any fillings that you would like.
Let the omelette cook until the eggs are fully set, 1-2 minutes, then gently roll the omelette and transfer to a plate. The surface should be smooth with no color.