Crack the eggs into a bowl, add the salt and water, and whisk well. Strain through a fine sieve if you want restaurant-smooth layers (optional, but it removes the stringy bits).
Heat a lightly oiled 20 cm nonstick or square tamagoyaki-style pan over medium-low heat. Wipe out excess oil with a paper towel — too much oil keeps the layers from sticking to each other.
Pour in a thin layer of egg, about 1/4 cup, tilting the pan to cover the surface.
Scatter a little scallion, carrot, and onion over one half while the egg is still mostly wet.
Once the egg is set but not browned, start rolling from the edge closest to you, using a spatula or chopsticks, pushing the roll to the far side of the pan.
Oil the empty area of the pan, pour in the next thin layer, and tilt so it flows underneath the existing roll.
Once that layer sets, roll again, this time incorporating the first roll, so it grows thicker with each pass.
Repeat until the egg is used up — usually 3 to 4 layers total.
While the roll is still warm, press it firmly with the spatula, or wrap it tightly in a bamboo sushi mat or a sheet of foil, to set the round shape. Rest 2 minutes before unwrapping.
Slice into rounds about 1.5 cm thick with a sharp knife.