Assemble your supplies. I like to use farmer's market eggs and organic butter. This walnut oil is also from a local producer who sells it at my local farmer's market, and is rich in flavor.
Chop a little butter into small pieces. You don't need a lot; maybe a teaspoon's worth or less. Some people use milk for this step, which is fine.
Rinse off the eggs.
Whisk the eggs in a bowl, add the butter, and, if you want, add herbs, cheese, or other ingredients. I sometimes add mushrooms (sliced thinly so they will cook with the eggs) and shredded cheese.
The scientific reason to add butter or milk is to help prevent long-chain proteins from forming and making the eggs tough. I add the butter in solid form, so that it melts as the omelette cooks.
Lightly whisk in the butter to separate it somewhat, so it's not one big clump, as well as to blend in any optional ingredients.
Put a high quality pan (one that conducts heat well) over a medium flame. I've found through experimentation that this 8" pan works well with 2 or 3 eggs. Your mileage may vary.
When water droplets dance on the surface for a second or two, it's the right temperature to add your oil.
This is a good time to push the toaster lever down if you're making toast to go with.
Add a bit of walnut oil to the hot pan. You can use other oils too, depending on what flavors you're going for. I use grapeseed oil when I have more delicate flavors or herbs.
Wait a few moments for the oil to heat, but don't let it smoke, then add your eggs. The eggs should sizzle and start to puff up nicely right away.
Add salt and pepper to taste.
Shake the pan so that the omelette doesn't stick to it as it starts to develop. You can use a fork to keep it moving or a rubber spatula if the sides start to stick.
Keeping the pan moving so the omelette won't stick, flip it over, like so. I usually do this over the sink as it can splatter a bit. (Mend any partially completed flips with a spatula.)
Return the pan tithe stove and cook a few minutes more until it's almost done to your liking. You can turn off the flame for the last 30 or 60 seconds so you don't overcook it.
I actually let this go just a little too long while I was photographing it.
Plate directly from the pan and eat right away. Adjust seasoning to taste.
Don't forget your toast. (Extra credit if it popped up just as you were finishing the eggs.) Or garnish with herbs and serve with Dijon mustard and a glass of wine for a French-style lunch.