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

Melt the butter in a non-stick pan over low heat.

Pour in the egg mixture and stir gently and continuously with a spatula.

Just before the eggs finish setting, stir through the grated cheese until melted and the eggs are soft and just set, not firm.

Remove from the heat while still slightly glossy, as they will continue cooking off the heat.

Serve immediately.