When I first started packing bentos, I could not make “nice” egg sheets. They were either brownish (like over cooked), or too thin to be folded, or there were a lot of bubbles on the surface. Then, I checked out my bento books and a few blogs, especially from akinoichigo, and found that we have to add some corn starch to the egg mixture, so that the egg sheets can be better formed. I can’t read Japanese, so hopefully, my translator is giving me the right translation! LOL!
Thus, I always add some corn starch to the egg mixture, before frying it. Here’s how I fix my egg sheets:

I separated the egg white from yolk. You don’t have to do this, unless you prefer white and yellow egg sheets.

Mix a teaspoon of corn starch in water. Then, add a teaspoon of diluted corn starch into the egg mixture. I can’t tell exactly how much water you need for the corn starch, but don’t make it too watery.

Stir the egg mixture well and “filter” it with a sieve.
Then, heat up your frying pan and add approximately a teaspoon of cooking oil. Try to “move” the oil around so that it covers most part of the frying pan. Once the oil is heated, set the stove to the lowest flame and pour the excess oil away.

Pour in the egg mixture on the frying pan.
Let it cook for a couple of minutes. If you see bubbles forming on the surface, lift up your pan and keep it a way from the flame. The bubbles should subside, and the surface of the egg sheet will look smoother.
After that, flip the egg sheet to the other side. Now, turn off the stove.

Cover the pan with a lid and let the other surface cooked by the “remaining heat” from the frying pan. It should be done in less than 3 minutes.
I think I saw this “trick” from a Japanese blog, but I can’t remember where it’s from. Since I can’t read Japanese, I did my egg sheets in trial and error and now I’m happy with the result:

My white and yellow egg sheets.
I would normally wrap the egg sheets (after they are cooled down) in cling wrap and keep them frozen in my fridge. They will stay fresh in a week, and it’s easier for me if I need them for bento decoration. Just thaw them a night before in the chiller and they are ready to be used on the next day.
Give it a try and let me know ya?
P/S: Here are some blogs with egg sheet tutorials:
Microwaved thin egg sheets (usuyaki tamago)
Japanese basics: thin omelette (usuyaki tamago)
How to make an egg sheet
