Beat eggs thoroughly in a bowl; whisk in dashi stock, sugar, mirin, and soy sauce until sugar has dissolved.

Place a nonstick skillet or omelet pan over medium heat. Oil the pan with vegetable oil. Pour a thin layer of egg mixture into the hot pan and swirl to coat pan.

When egg layer is firm on the bottom but still slightly liquid on top, lift up about 1 inch of the edge of the omelet with a spatula and fold end over remaining egg layer; continue rolling the omelet to the end and push the roll to the edge of the skillet. Oil the skillet again if it looks dry; pour another thin layer of egg into the skillet and lift the roll to let the egg flow underneath the omelet roll. Fold the omelet roll over the new layer of egg, continuing to roll to the end as before. Push omelet to edge of skillet.

Pour a new egg layer into the skillet, oiling the pan if needed. Roll the omelet over to incorporate the next egg layer into the roll. Pour new layers and roll into the omelet until all egg mixture has been used. Remove omelet to a serving platter and cut into 6 equal pieces to serve.