In a mixing bowl, whisk together the eggs, soy sauce, mirin, sugar, and a pinch of salt and pepper until well combined and slightly frothy.

Heat a non-stick skillet over medium heat and add 1 teaspoon of vegetable oil, swirling to coat the bottom.

Pour a thin layer of the egg mixture into the skillet, just enough to cover the bottom. Cook for about 1-2 minutes until the edges start to set but the center is still slightly runny.

Using a spatula, gently roll the omelet from one side to the other, creating a log shape. Push the rolled omelet to one side of the skillet.

Add another teaspoon of oil to the empty side of the skillet, then pour another thin layer of the egg mixture into the pan, lifting the rolled omelet slightly to let the new mixture flow underneath.

Cook for another 1-2 minutes, then roll the omelet over the new layer, repeating the process until all the egg mixture is used.

Once cooked, remove the omelet from the skillet and let it cool slightly before slicing into pieces.

Garnish with chopped green onions before serving.