Combine eggs, salt, and water in a mixing bowl. Whisk for 1 or 2 minutes, until whites are completely blended.
Heat 1 1/2 tablespoons butter in a 9- inch nonstick skillet over medium-high heat. Once the butter has melted and before it starts to sizzle, pour in the eggs. Using a rubber spatula, lift and scramble the eggs, scraping the edges and bottom of the pan while shaking it in a circular motion so the eggs cook slowly and evenly.
Reduce heat to low and smooth the eggs to create an even thickness with a surface that is wet but not runny.
Remove the pan from heat and use the spatula to begin rolling the omelet, starting at the handle side of the pan. Roll about 3 times until the omelet is 2 inches from the opposite side of the pan. Fold the last flap of egg over the top of the cylinder, leaving the seam side up. Add 1/2 tablespoon buter to pan, melting it under the omelette.
Slide the omelette to the edge of the pan and flip onto a plate with the seam side down. Brush the outside with a bit more butter. Garnish with herbs and serve.
Adapted from Allrecipes.com, Chef's John's French Omelette.