Heat the skillet at medium high temperature and spread a light layer of oil on, using kitchen paper or a pastry brush.
In the meantime prepare the omelette: in a small bowl, whisk together soy sauce, mirin and sugar.
In a large bowl whisk the eggs gently, using a fork or chopsticks. Fold in the soy mixture and mix until all ingredients are just combined.
Pour a thin layer of egg mixture in the skillet. Swirl it around like you would do for a french pancakes. Then, roll it into a log and move it to the end of the pan.
Pour some more egg mixture to cover the rest of the pan. Lift up a bit the egg roll, and let some of the egg mixture go under it too (so that they stick together). After the new layer has set (but still slightly uncooked in the middle), roll the log back onto the the already made egg roll, and move to the end of the pan.
Repeat the process, one thin layer at the time, until all the egg mixture is used up.
In the meantime, cover with cling film a bamboo mat. Once your omelette is ready, gently remove from the pan onto the prepared bamboo mat.
Roll the omelette tightly, pressing a little on top to make the rectangular shape, just how you would do for sushi.
Allow to cool and set, then cut the omelette into large bites. Thread the omelette chunks onto sticks and serve immediately.