Heat the clarified butter in a skillet over a medium-high flame. Whisk the eggs, salt, and freshly ground pepper together very well while the pan is heating, not before. If they have to sit and wait for the pan, the whisked eggs will deflate. You want to incorporate lots of air into the mixture so that your omelet is light and fluffy.
Place your hand immediately above the skillet. When your palm feels warm, the skillet is ready to start cooking. Working fast, pour the whisked eggs into the hot skillet. Reduce heat to medium. Simultaneously, whisk the eggs and shake the skillet vigorously back and forth over heat for less than a minute. You want to keep the eggs moving, incorporating some of the runny parts with the more-cooked parts until there are some curds swimming in the eggs. Stop whisking.
Continue cooking, being sure eggs cover the entire surface of the skillet, using a rubber spatula to push together any holes that may have formed.
Run the rubber spatula along the right side of the omelet to loosen eggs from the skillet. Place the spatula under the right side of the eggs, making sure that the spatula is well underneath the eggs to offer maximum support, and lift the right side over the left in one fluid motion. The folded omelet should look like a half moon.
Lightly press down on the omelet with spatula to seal the omelet together. Do not press hard; you do not want to flatten the curds. Check to make sure the handle of skillet is still facing directly out toward you.
Lift up the skillet with one hand, and hold the plate with your other hand. Tilt the skillet, and let the curved edge of the omelet slide onto the plate. Quickly invert the skillet, folding the portion of the omelet that is left in the skillet over the curved edge already on the plate. Keeping the skillet about stomach level with the handle facing directly out should help you do this. Garnish with a parsley sprig.