In a small bowl, whisk together the dashi/water, sake, sugar, tamari, and salt to taste until the sugar is dissolved.
Add to the eggs and stir to combine. Transfer the mixture to a measuring cup/container with a spout.
Heat a tamago pan** over medium heat. Add 1/2 teaspoons oil and brush over the surface of the skillet with a pastry brush. Working in batches, pour a thin layer of egg*** into the skillet.
Tilt the pan to coat the surface evenly with egg. Place some spinach leaves on top of the egg. When the egg begins to pucker, around the edges, push/roll the egg with chopsticks or spatula from one end of the pan to the other so that you have a long cylinder of egg. Leave it in the pan.
Brush the pan with more oil. Pour more egg in the pan and tilt it to spread the egg around. Lift the egg log and let the egg run underneath (it will help the rolling process).
Spread more spinach leaves on top of the egg and, once the egg starts to pucker, use the egg log as your core and roll in the other direction.
Repeat the process, fattening the log as you go. Watch your heat and lower it towards the end to prevent the log (as it gets bigger) from browning too fast due to its weight.
Remove the log from the pan and cut into 8 equal pieces.