In a medium bowl, combine water (2 Tbsp), sugar, mirin, salt, and rice vinegar (1/4 tsp). Mix until sugar is dissolved. Add eggs, and mix very well.

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 the 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. Add oil as needed. Pour 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 set 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 completely.

Cut the egg log in half. Then slice 1/4" thick (6-7 mm) vertical slices, and get at least 12 pieces. Set aside.

Cut Nori into 5" x 1/3" (about 13 cm x 1 cm) strips. Set aside.

Mix 1/4 cup vinegar and 1/4 cup water in a small bowl. Lightly wet or dampen hands with the vinegar mixture, and take a golf ball size piece of Sushi rice (about 2/3 oz or 20 g). Form into an oblong shape. Repeat to make 12 pieces. Top each rice ball with a slice of egg, and wrap around with Nori strips. Serve with Soy Sauce and Wasabi for dipping if you like.