1. In a bowl, whisk together the eggs, sugar, mirin, soy sauce, and salt until well combined.
2. Heat the tamagoyaki pan over medium heat and lightly oil it with vegetable oil.
3. Pour a thin layer of the egg mixture into the pan, tilting to cover the bottom.
4. Once the egg is set, roll it to one side of the pan.
5. Add more oil if needed, then pour another thin layer of the egg mixture into the pan, lifting the rolled egg to let the uncooked egg flow underneath.
6. Once set, roll the new layer together with the previous roll. Repeat until all the egg mixture is used.
7. Remove from the pan and let it cool slightly before slicing.