There's an extra ingredient to a good omelette that almost all professional and celebrity cooks miss out on, very few include it in the recipe, yet it makes a massive difference to quality and texture for almost any kind of omelette.
Simply add two or three tablespoons of plain old tap water to the whisked egg mix, then mix it some more. The water gives a wonderful, more aerated, fluffy texture.
A lot of these 'professional' cooks are mashing around with forks or spatulas while cooking it - not needed.
To that end, here's how I consider to make a good, thin omelette.
2 -3 eggs whisked in a tall drinking glass (bowl usually always spills, easier to pour evenly from a glass and to find any rogue egg shell)
Add black pepper to preference - whisk again. I just use a plain old table fork for whisking.
Add 2- 3 tablespoons of water - whisk more.
Heat thin layer or oil or butter in a large flat pan, 10" or 12" or as big as you have to hand.
Pour recently whisked mixture over the pan letting it evenly lay.
Let it sit on a low heat, don't touch it at all unless to angle pan to even the egg mix.
You'll notice the bottom cook, when the top is still liquid add any toppings - rubbery Dutch or Norwegian cheese like Emmental or Jarlsberg is best.
Just tear a couple of slices up and chuck that on there - you can add ham too or anything else, cooked mushrooms or onions (cooking mushrooms or onions within the omelette usually discolours the egg or affects its structure; adding it later like this is better.)
Then take off the hob immediately and put under the grill. Observe and don't let it brown.
When done either fold over once or roll it up to look like a crepe, then serve.
I promise you, it's better, easier and quicker than what that woman cooked in the Mythbusters video.