Crack the eggs into a bowl, add milk or water, salt, and pepper, and whisk until frothy.
Dice the ham and shred the cheese, setting them aside for easy access during cooking.
Heat a non-stick skillet over medium-low heat and melt the butter, coating the pan evenly.
Pour the egg mixture into the skillet, allowing it to sit undisturbed for 20 seconds.
Gently stir the edges toward the center, tilting the pan to allow uncooked egg to flow underneath.
When mostly set but still slightly runny, sprinkle the diced ham and shredded cheese over half of the omelette.
Carefully fold the omelette in half and let it cook for an additional 30 seconds.
Slide the omelette onto a plate, garnish with parsley or chives, and serve immediately.