In my experience, the biggest problem beginning omelette-makers have is that they end up making something that is between an omelette and scrambled eggs. No. Pick one or the other.
For the record, I vastly prefer my scrambled eggs to my omelettes, but my wife loves my omelettes and they've received plenty of compliments from others too.
First, tools and ingredients. I use a dedicated non-stick pan for eggs (8-inch diameter, I'm guessing). Seriously, I've had it for more than 10 years and nothing other than eggs has been cooked in it. In this pan, I have to use at least 3 large eggs to make a decent omelette, otherwise there's not enough stuff cooking to make things work. I can make up to a 6-egg omelette, but at that point I usually get better results making two 3-egg omelettes. Of course, the eggs should be fresh. Also, many will recommend that you start with eggs that are at room temperature. (For morning eggs, get up early, set your eggs out on the counter, go back to bed for an hour.) I haven't decided whether this has detectable results or is just superstition.
Also, I'm taking classical omelettes here, not "fluffy" omelettes, which I don't particularly like and have never cooked myself. We call them "brain omelettes" because when done right, they look like sulci and gyri.
To me, the differences between omelettes and scrambled eggs:
Omelettes:
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Are cooked relatively quickly over medium-to-higher heat
Add
water Eggs have *not* been beaten into a single consistency
Are never stirred
Can be cooked (if you absolutely insist) until lightly browned
Scrambled eggs:
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Cooked relatively slowly over medium-to-lower heat.
Add milk
Eggs have been beaten into a single consistency
Are stirred (how much depends on the size of curd desired)
Do not cook until browned
Let's cook.
Omelettes:
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Break at least 3 large eggs into a bowl. Add 1 teaspoon of water per egg. Puncture the yolks with a fork, then beat no more than 30 strokes. The idea is that you still have some strands of white and yolk, not all a single consistency. (I use the count of 30 to prevent me from beating them too much.)
Pour into into your heated pan (medium-to-higher heat) that has a little bit of fat in it (butter, olive oil, etc.) Do nothing for about 30 seconds. Then use something (heat-resistant spatula, wooden spoon, etc.) to pull 4 sections of the egg (north, south, east and west) to the center. Liquid egg should run to fill the places on the pan that you exposed. If not, tilt the pan so it does. After that cooks, pull 4 more sections to the center, usually 45 degrees off-set from the first pulls, and let that cook. Repeat as necessary. It's these little flows that create the characteristic folds.
Cook until bottom just starts to brown. Top is still very moist but should not have runnable liquid.
You're done cooking. Fold omelette in half while sliding onto a plate.
In the past, I used to flip the omelette in the pan by tossing up into the air (it's fun to practice!) and cook the other side for a few seconds. I've now decided that that's unnecessary (though impressive to onlookers).
Note: if you've got the heat too high, you'll probably get a big bubble during the initial 30-second do-nothing period. If you've got the heat too low, when you try to pull the egg to the center, there won't be enough cooked to pull.
Scrambled eggs:
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Break at least 2 large eggs into a bowl. Add 1 teaspoon of milk per egg. Puncture the yolks with a fork. Beat until a single consistency. (I don't count the strokes.)
Pour into into your heated pan (medium-to-lower heat) that has a little bit of fat in it (butter, olive oil, etc.) Do nothing for about 30 seconds. Then use something (heat-resistant spatula, wooden spoon, etc.) to stir the eggs.
I stir the cooked part of the eggs into the center of the pan. Then let them cook some more. Then stir into the center again. Only a few cook/stir cycles are necessary. They're done when you have a single mass with still-creamy egg on the outside. The goal in my scrambled eggs is a single large curd (it's beautiful when you slice through it on the plate!) that still has creaminess. (Detractors would say my scrambled eggs are "runny." I personally don't have issues eating undercooked eggs that I've made myself, and in fact I prefer them that way.)
The "constantly stirring" school of scrambled egg-ology would have you, well, constantly stir the eggs. This is fine if you prefer lots of small curds instead of one large one like I do.
Under no circumstances cook until rubbery or brown.
Further thoughts:
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For me, I add salt and pepper to the eggs before beating. For my wife, I don't. She prefers salting and peppering at the table.
Oh, fillings. My thoughts on filling an omelette are that if you have to add a filling, you haven't done a good job with the eggs in the first place. A good plate of eggs will stand on their own. OK, I'm only about half serious with that. Cook the filling separately then add to the top of half of the omelette at the very end, right before folding and sliding it onto a plate.
I'll also mix things into my scrambled eggs. My latest fascination is Genoa salami.
For the record, the best scrambled eggs I ever had in my life (and probably one of the best breakfasts ever) was at an inexpensive bed-and-breakfast in Keswick, England. It was a variation of a classic English breakfast. There was a link of organic Cumberland sausage made by friends of the proprietors. There was a grilled tomato fresh from their vegtable garden. The garnish (which I ate, of course!) was a sprig of rosemary from their bush. The scrambled eggs were deliciously creamy, cooked
au bain marie. (My only experiment cooking scrambled eggs
au bain marie gave miserable result. Must be some tricks to work out.)
One of my favorite "comfort meals" is omelettes or scrambled eggs, a simple salad, and crusty bread. My simplest salad: washed and spun Romaine lettuce, salt and pepper, a splash of rice wine vinegar, a couple of slivers of red onion, and a crouton or two if you're feeling decadent. Get the vinegar/salt balance right and you don't need to bother with oil. Seriously.
I'm off to the grocery. I'm making lavender shrimp for lunch.