This recipe works best in a French omelette pan, but a skillet can be used. Look for an omelette pan that is seven inches in diameter at the bottom.
Try experimenting with various toppings: For example, beat in a tablespoon of minced chervil, parsley, chive, or tarragon together with the eggs for an herb omelette; or once the eggs have set, sprinkle some cheese, diced sautéed potatoes, ham, or mushrooms over the top. Some other toppings that are worth a try include asparagus tips, artichoke hearts, diced cooked shrimp, crab, or lobster. Or, for a truly decadent omelette, sprinkle cheese over the finished omelette, dot with butter and finish underneath the broiler.
Once you feel that you've mastered this technique, try something more challenging.
Beat the eggs and seasonings in a bowl for 20-30 seconds, until the whites and yolks are just blended.
Heat the butter in a pan over very high heat. (If you have an electric stove, it should be red hot.) As the butter melts, tilt the pan in all directions to film the sides. Wait until the foam has almost subsided, and the butter is about to brown. Add the eggs to the pan.
Holding the pan handle with your left hand, thumb on top, slide the pan back and forth rapidly over the heat. At the same time, with a fork in your right hand (making sure to keep its flat side against the bottom of the pan), stir the eggs quickly to spread them all over the bottom. In 3-4 seconds, they will become a light, broken custard. (A filling would go in at this point.)
Then, tilt the pan at a 45-degree angle away from you, and rapidly gather the eggs at the far end of the pan with the back of your fork. Keeping the pan tilted, run your fork around the lip of the pan under the far edge of the omelette to be sure it doesn't stick.
Give 4-5 short, sharp blows on the handle of the pan with your right fist to loosen the omelette, and make the far edge curl over onto itself.
Hold the pan tilted over heat for 1-2 seconds to brown the bottom of the omelette very lightly (but not too long or the eggs will overcook). The center of the omelette should remain soft and creamy.
Turn the omelette over onto the plate, rub the top with a bit of butter, and serve immediately.