Heat up bonito stock and mix light soy sauce, mirin, salt and white sugar. When salt and sugar are dissolved remove from heat and cool it down in iced water.
Slice shiitake mushroom and sauté in a pan with touch of soy sauce and when nearly cooked add eel and heat through. Remove from heat and set aside.
Whisk eggs gently with chopsticks and then add cold bonito stock mixture and stir to combine.
Strain egg mix through a sieve.
Preferably using a Japanese square egg omelette pan heat and grease lightly with oil.
Add one ladleful of egg to pan and spread evenly, popping any bubbles with chopsticks.
Top with layer of mushroom and eel mixture in the middle of egg and then flip egg to cover mushrooms and push rolled mix to one side.
Grease remaining pan, slide omelette onto greased side, grease again and repeat process four or five times, being carful to lift the omelette and allow the egg to run underneath each time.
Roll up omelet with sushi bamboo sheet for 10-15min until it is set.
Cut into small slices and plate up. Drizzle teriyaki sauce over omelette