Mix eggs, salt, soy sauce and Mirin in a bowl.

Heat a pan at medium high temperature and add oil. (A rectangular Tamagoyaki pan is best, but a round pan can work as well.)

Pour a thin layer of egg mixture in the pan, tilting to cover the bottom of the pan. After the thin egg has set a little, gently roll into a log. Start to roll when the bottom of the egg has set and there is still liquid on top. If you let the egg cook too much, it will not stick as you roll the log. Now you have a log at one end of the pan. Pour some more egg mixture to again cover the bottom of the pan, with the roll of egg at the end. After the new layer has set, roll the log back onto the the cooked thin egg and roll to the other end of the pan.

Repeat adding egg to the pan and rolling back and forth until the egg is used up.

Remove from the pan and cool for 3-4 minutes.

Slice the ends of the log off and then slice the log into 1/2" pieces. You should see a nice spiral pattern in the cross section of the egg.