Crack the eggs into a bowl and beat with a fork just until you have an even mixture (no traces of white can be seen). Season with salt and pepper.
Place a 20.5 centimeter nonstick skillet over medium-low heat, then add the butter, and swirl evenly to coat pan. As soon as the butter has melted and is foaming slightly, add the eggs to the skillet, then turn heat down to low. Using a fork positioned with the tines tilted upwards so they do not scrape the pan, start stirring the eggs, occasionally shaking and swirling the pan (the goal is to allow the uncooked parts of the egg mixture to make contact with the pan so that the omelette cooks evenly). Scrape down the sides of the pan regularly as well. Once the surface of the omelette looks creamy, but not raw, it’s ready. Tilt the pan away from you, then, using a silicone spatula, carefully roll up the omelette.
Carefully slide the omelette off the pan onto a serving plate, seam side down. Garnish with chopped chives and sea salt flakes and serve immediately.