In a medium bowl, whisk together the eggs, milk (if using), and salt. Whisk using a side-to-side motion until uniform in appearance, do not over mix.
In an 8-inch nonstick skillet, heat the butter over medium-high heat until it just begins to bubble and foam, but does not brown.
Add the eggs to the pan, use a spatula to immediately pull the cooked curds from the pan's edges toward the center, allowing the raw egg to run underneath, tilting the pan to help move it to the bottom. Start from the top of the pan and create curds around the entire omelet, about 1 to 1 ½ minutes.
Once the eggs mostly cook, similar to soft scrambled eggs with a glossy and slightly wet surface, turn the heat down to low.
Sprinkle the cheese on one half of the omelet. Using a spatula, fold the other half on top. The surface will be golden brown.
Transfer to a plate and garnish with pepper and chives, serve immediately.
French-Style Omelette
In a medium bowl, whisk together the eggs, milk (if using), and salt. Whisk using a side-to-side motion until uniform in appearance, do not over mix.
In an 8-inch nonstick skillet, heat the butter over medium-low heat until it just begins to bubble and foam, but does not brown.
Add the eggs to the pan, then wait for 10-seconds until the edges begin to set. Use a spatula to pull the cooked curds from the pan's edges toward the center, allowing the raw egg to run underneath. Tilt the pan as needed. Start from the top of the pan, and work to create curds around the entire omelette, about 2 to 2 ½ minutes.
Once the eggs mostly cook, with a glossy surface, turn the heat off.
Using a spatula, fold one side to the center, then the other side, creating a rolled shape. The surface should not be browned.
Invert the omelette onto a plate with the seam-side down. Garnish with pepper and chives, serve immediately.
Notes
Adding Liquid: This makes the egg softer and more tender but lessens the egg flavor. Dairy also adds extra richness.
Saltier Eggs: Use ¼ teaspoon of kosher salt instead of 1/8 teaspoon.
For Cooking 3 to 4 Eggs: Use a 10-inch skillet and look for the appearance change. The cook time will be seconds.
Adjusting Batch Size: For every large egg, use ½ teaspoon butter or oil and 1/16 to ⅛ teaspoons of salt. See pan size recommendations in the full article.
For a less browned surface on the American-style omelet, use medium instead of medium-high heat.