Crack eggs into a medium bowl and whisk vigorously for 30 seconds until completely smooth and slightly frothy. Add milk, salt, and pepper, whisking until well combined. The mixture should look creamy and uniform without any streaks of egg white.

Place an 8-inch non-stick pan over medium-low heat and add butter. Let it melt completely, swirling to coat the entire bottom. The butter should sizzle gently but not brown - this indicates the perfect temperature for fluffy eggs.

Pour the egg mixture into the heated pan. Let it sit undisturbed for 20 seconds, then gently stir with a rubber spatula, pushing cooked edges toward the center while tilting the pan to let uncooked egg flow underneath. Continue this process for 2-3 minutes until eggs are almost set but still slightly wet on top.

If using cheese or herbs, sprinkle them over one half of the omelette. Using your spatula, carefully fold the omelette in half, creating a perfect half-moon shape. The residual heat will finish cooking the eggs and melt the cheese beautifully.

Slide the omelette onto a warm plate and serve immediately. The texture should be creamy inside with a tender, golden exterior.