Mix the eggs well. Then add dashi, soy sauce, mirin and salt mix well again.
Heat a Japanese omelet pan (or small frying pan) and thoroughly coat the surface of the pan with a paper towel soaked in the oil. Drop a small amount of the egg mixture in a frying pan to check if sizzles, which indicates the temperature of the frying pan is appropriate.
Pour ¼ of the egg mixture into the frying pan and then allow the mixture to thinly cover the surface of the frying pan. Once the egg mixture gets mostly cooked but still slightly runny, put eel on the far end of egg.
Using turner, fold egg sheet with egg from the far end to toward you.
Oil the half top of the frying pan that is not covered by the egg mixture and move the cooked egg mixture toward the top. Oil the bottom half and add other ¼ of the egg mixture to the empty part of frying pan. Repeat the procedures for another 2 times until you finish egg mixture. Cut into 4 pieces.