Combine eggs, mirin, soy sauce, and sugar. Whisk until well combined.
Heat oil over medium heat. Using a balled-up paper towel, carefully wipe the oil over the surface of the pan and save to grease the pan for each new layer.
Scoop 3 tbsp of the egg mixture and quickly tilt pan and swirl egg mixture to create an equal layer. Cook for 1 minute. Using a rubber spatula, loosen the egg all around the edges, then carefully fold the top of the omelet ¼-inch towards you. Keep folding/rolling the egg over itself until you have a narrow, rectangular omelet at the edge of the pan nearest you.
Reduce heat to medium-low and lightly grease the exposed area of the pan. Add 3 more tbsp egg mix to the exposed area of the pan, swirling it around to create another layer. Lift the folded eggs with the spatula to allow the raw egg mixture to run under the omelet.
Once the new layer is set, gently roll the folded owlet away from you in three to four flips. Repeat the whole process three more times, lightly greasing the pan each time with the greased paper towel.
Transfer omelet to a cutting board. Trim ends if a round skillet was used. Cut crosswise into 4 equal slices. To serve, place 2 slices on a plate, cut-side up to show egg layers.