Preheat the skillet for several minutes over low-medium heat. (I use the 4 setting.)
In a small bowl, beat an egg until the yolk and whites are fully combined. Optionally, season the mixture with salt and other seasonings.
Lightly grease the preheated pan.
Pour the beaten eggs into the skillet, swirling immediately to create a thin, even layer.
Allow the eggs to cook undisturbed until they are fully set. (1-2 minutes)
When the edges of the egg wrap start to peel up and the egg on the top layer has set, carefully flip the egg wrap with a spatula.
Cook lightly on the other side for around 30 seconds.
Once cooked, let it cool slightly before adding your favorite fillings. (Once cooled, they will become more pliable.)
Video
Notes
Expert tips
You can stack your egg wraps for bringing out to the table.
I use an 8-inch (20cm) cast iron skillet to prevent sticking without the toxicity of a non-stick pan. To make sure the egg doesn't stick, preheat it on a medium-low setting for several minutes before greasing the pan. If the pan isn't properly pre-heated, the first wrap will stick, and it will be difficult to flip and remove it.
Very lightly grease the pan. (I generally use tallow, lard, or ghee.) If you add too much fat, the egg will float and won't adhere to the pan. This will prevent you from swirling the egg mixture evenly across the bottom. It isn't necessary to grease the pan again before making each wrap. Instead, grease the pan when the bottom is dry, generally after every 2-3 wraps.
If you find that it is taking too long for the egg to cook and release, very slightly increase the temperature of your pan. If it is browning before fully cooking and releasing, lower the temperature slightly.
If the egg is bubbling and making it impossible to get an even layer across the bottom of the pan, the temperature is likely too high. Lower the heat. You can fix large bubbles by piercing them and filling the void with some beaten egg mixture.
If you find that one egg isn't enough to cover your skillet, have another beaten egg prepared, so you can add more beaten egg to your wrap as needed. 1.25-1.33 eggs per wrap is a good estimate.
If you break a wrap while trying to flip it (generally when you are impatient and try to flip too soon), you can mend it with some beaten egg. Flip again after cooking it to ensure the bond is fully cooked on both sides.