Place an omelet pan over medium heat for 1 minute. While it's heating, beat the eggs in a small bowl, adding the salt and herbs.
Add the butter to the pan and let it melt. Tilt the pan in all directions to distribute the butter, then pour in the egg mixture, keeping the heat to medium.
As eggs begin to set at the edges, carefully push cooked portion toward the center of the pan with a small spatula. At the same time, tilt the pan, allowing any remaining raw egg to fill spaces.
As soon as the egg stops flowing, sprinkle the grated cheese onto half the omelet. The egg mixture should still be moist, as it will continue cooking when removed from the pan and you don't want it to overcook and become leathery.
Use the spatula to fold the omlet in half and slide or flip it onto a plate. Serve immediately, sprinkled with freshly ground pepper to taste.