Reverse engineer the Perfect Japanese Omelet
It's called an "omelet", but it's scrambled eggs, well formed into an omelet shape

Cook scrambled eggs, and just before they set (20 ish seconds) fold them, and tip the pan to roll them in the curve of the pan to form the classic omelet shape and serve. Since the eggs are not yet fully set, the outer surface will form a smooth omelet appearance

You need a pan with large lip, and gentle curve to achieve a nice uniform shape. After the initial cooking phase, tipping the pan is required to ensure the eggs mold into the curve of the pan, and the also have a reduced heat to stop over cooking (you don't have time to turn down the heat anyway, so tipping does it all)

If the surface is not smooth you have cooked it too long before folding, or you did not beat the eggs sufficiently. Eggs that have been fully cooked before folding cannot form a smooth skin surface, and eggs that are not fully beaten will never form a smooth surface as the different proteins congeal (denature) at different rates and elasticities

Omelet's are handled gently, scrambled eggs are handled more vigorously, and over a much higher heat. This type of egg dish requires the scrambled approach to start, and the omelet approach to finish