Slice onions finely.
Heat oil in a non-stick frying pan set over very low heat. Add onions and stir to cook frequently, until onions turn soft. Do not allow to brown.
Sprinkle mirin over onions and continue cooking until onions become sticky and golden.
While the onions are cooking, crack eggs into a bowl and add the salt and pepper. Beat well.
Distribute onions evenly over pan. Turn up heat to medium and add eggs to the pan with the onions.
Stir gently with a spatula while swirling the pan. Do this until the surface is just set and the underside is golden brown.
Flip the omelette over to cook the other side.
Slide onto a plate and either leave whole to serve, or cut it up into quarters.