Mix eggs, sugar, salt, soy sauce and mirin in a bowl.
Heat your pan at medium high temperature.
Add oil, and using a folded paper towel, make sure to evenly coat your pan. Set your oiled paper towel aside. You will use it to grease the pan as needed.
To check if the oil is hot enough, use the “sizzle“ test by dropping a small amount of the egg mixture into the pan. When you hear a sizzling sound, the pan is ready.
Pour a thin layer of egg mixture in the pan, tilting the pan to ensure you cover every inch of the pan.
When the bottom of the egg has set a little, with still a bit of liquid on top, start to gently roll the egg. Note: If you let the egg cook too much, it will not stick as you roll the egg into a log.
You should now have a log at one end of the pan.
Grease the bottom of your pan using your oiled paper towel.
Pour another thin layer of egg mixture to again cover the bottom of the pan. Lift the log gently, while tilting the pan to allow the mixture to cover the pan underneath the log.
After the new layer has set, again still with a little bit of liquid on top, gently roll the log back onto the cooked thin egg.
Push the roll to the other end of the pan.
Repeat adding egg mixture to the pan and rolling back and forth until all the egg mixture is finished i.e. repeat steps 8 to 11.
Remove from the pan.
Transfer the tamagoyaki onto a cutting board.
Optional: To help set its shape, place a paper towel and a bamboo sushi mat on top of your tamagoyaki. Then, wrap the paper towel and bamboo sushi mat around the tamagoyaki while it’s still hot.
Let it stand for 5 minutes to allow the residual heat to finish cooking the egg and to cool slightly.
Slice the ends of the log off and then slice the log into 1/2″ pieces.