Crack the eggs into a mixing bowl. Add milk, salt, and black pepper. Whisk well until the mixture is smooth and slightly frothy.

Prepare any fillings. If adding vegetables, chop them finely. Shred the cheese and chop the herbs if using.

Heat the non-stick frying pan over medium heat. Add the butter and let it melt, swirling to coat the pan evenly.

Pour the egg mixture into the pan. Let it cook undisturbed for about 30 seconds until it just starts to set around the edges.

Using the spatula, gently stir the eggs, pulling them from the edges toward the center. Tilt the pan to let uncooked egg fill in the gaps.

When the surface is still slightly runny, sprinkle cheese, vegetables, and herbs over one half of the omelette.

Cook for another 1-2 minutes, until the omelette is mostly set but still a bit soft in the center.

Carefully fold the omelette in half with the spatula. Slide it onto a plate and serve immediately.