In a bowl, whisk together the eggs, soy sauce, maple syrup, water, and salt until well combined. You don’t want to whip too much air into the eggs, but whisk until smooth. (Optional) Strain the mixture through a fine-mesh strainer to make it extra smooth.
Heat a tamagoyaki pan or small nonstick frying pan over low to medium-low heat. Lightly coat the pan with oil. It’s convenient to use a paper towel folded into a small pad and dipped in oil to spread the oil evenly.
Pour ⅓ of the egg mixture into the pan and tilt the pan to spread it evenly. Pop any large bubbles with chopsticks.
When the egg is mostly set but still slightly soft on top, roll it from the far side to the near side. Use chopsticks or a spatula to support the egg and lightly tilt or toss the pan to help it roll. Then slide the log to the far side.
Oil the empty part of the pan well. Pour in another ⅓ of the egg mixture, lifting the rolled egg slightly and tilting the pan, so the new egg flows underneath.
When the new layer is mostly set, roll the egg back over the new layer. Oil the pan again and repeat with the remaining egg mixture.
Remove from the pan and let it rest for a few minutes. Slice into pieces and serve.
Optional: While the tamagoyaki is still hot, transfer it to a makisu, a bamboo sushi mat. Carefully roll it to shape. Let it cool to set before slicing.