Beat the eggs and season with salt and pepper. Melt the butter in a frying pan approximately 10 inches in diameter.
When the butter has melted and is bubbling, throw in most of the shredded mint, saving some for sprinkling on top at the end. When it has sizzled in the butter and become vibrantly green, pour in the beaten eggs and tip the egg around the pan.
Crumble the cheese over the omelette and cook, lifting the sides and swilling the pan around to let any runny egg cook in the heat underneath.
When the top of the omelette looks nearly set but still gooey, fold into thirds lengthwise — in other words, fold in two sides, leaving a strip of white-blobbed omelette facing up in a strip in the middle — and slide onto a plate. Sprinkle with the reserved mint and eat.