In a medium bowl, beat the eggs with the salt until well combined.
In an 8-inch nonstick skillet over medium heat, melt the butter.
Pour the beaten eggs into the skillet. Let them sit undisturbed for about 30 seconds until the bottom starts to set.
With a heatproof spatula, gently push the eggs from the edges toward the center, tilting the pan to allow uncooked eggs to flow to the edges. Continue this until the eggs are softly set but still slightly runny in the middle.
Remove the pan from heat. Tilt the skillet and use the spatula to roll the omelette into a cylinder. Slide the omelette onto a plate, seam side down.
Top with additional butter. If you prefer herbs, sprinkle finely chopped chives or parsley on top when serving.