Beat eggs in small bowl with fork or wire whisk until yolks and whites are well mixed.
Heat butter in 8-inch skillet over medium-high heat until butter is hot and sizzling. As butter melts, tilt skillet to coat bottom with butter.
Quickly pour eggs into skillet. While rapidly sliding skillet back and forth over heat, quickly stir eggs with a fork to spread them continuously over the bottom of the skillet as they thicken. When they are thickened, let stand over heat a few seconds to lightly brown bottom of omelet. Do not overcook... the omelet will continue to cook after being folded. Sprinkle with cheese.
Tilt skillet and run a spatula under edge of omelet, then jerk skillet sharply to loosen omelet from bottom of skillet. Fold portion of omelet nearest you just to center. Allow for a portion of the omelet to slide up side of skillet. Turn omelet onto warm plate, flipping folded portion of omelet over so far side is on bottom. Tuck sides of omelet under if desired. Sprinkle with salt and pepper and additional cheese if desired.