Crack the two eggs into a small bowl and beat until well-mixed.
In a separate bowl, mix starch, sake, and salt. Stir until all lumps are dissolved.
Pour the mixture into the beaten egg and mix briefly.
Add the oil for the omelet to the frying pan and put on medium low heat.
Pour the beaten eggs into the pan. Tilt the pan so they are distributed across the whole surface, as if you were making a pancake.
When the surface of the egg is still a little runny, turn off the heat.
Add the filling from earlier on top of the egg. Distribute it along a line the middle, like a hill from one side to the other. There should be an even amount of space to its left and right side. They will be folded to cover the filling over the next steps.
Lift one side of the omelet up with a spatula and flip it onto the filling to partially cover it.
Now it's time to move the Tonpeiyaki onto the surface on which it will be served, and finish folding it in the process. With the still round (non-folded) side first, slide the omelet out of the pan and flip the filling over it using a spatula from the other side. It should be a fast, but gentle motion. Both sides should now be tucked under the omelet, with the filling and a gap in the egg at the bottom.