In a small pan (use one that is the same diameter or slightly smaller than your serving bowl), add onion, dashi, sake, mirin, salt, soy sauce and cook for 5 minutes at medium heat.
Lightly beat eggs in a small bowl. Add the eggs to the pan with the onion mixture.
Wait until the eggs start to coagulate – about a minute. Slowly push the edge of the egg mixture to the center of the pan with a spatula, cover with a lid and reduce heat to low, continue to cook for approximately 30 seconds.
Fill serving bowl with cooked rice and slide omelette with sauce on top.