Combine all the ingredients (except the eggs and vegetable oil), in a small saucepan and heat until everything is dissolved and well mixed. Remove from the heat and allow to cool to room temperature. Mix the eggs together but try not to whip too much air into them while doing so because the completed omelet should be solid and thick, not light and fluffy. This omelet should be made with a traditional Japanese square pan (tamago yaki nabe), but if you don't have one a small Western style pan will do just fine (the finished omelet you will cut into oblong squares). Heat the square skillet or Western style frying pan and add a little vegetable oil using a swab of paper towel (the pan is ready when a test drop of egg sizzles). Pour in 1/3 of the egg mixture, tilting and rotating the pan so that the egg spreads across the pan's bottom in an even layer. When the surface of the egg sets and it's dry around the edges, use a pair of chopsticks (or a spatula), to roll up the omelet to one side of the square pan. Wipe in some more vegetable oil on the empty part of the pan. Add another 1/3 of the egg mixture and tilt to cover the surface of the pan, allowing the egg to cook. When the surface of the egg sets use the chopsticks to once again roll up the omelet... this time rolling the already cooked egg pushed to one side of the pan, over the newly cooked egg. Cook the omelet for just a few more moments and then remove from the fire and allow to cool. Once the omelet is cool you can cut it into oblong square blocks. Place on a platter and refrigerate until well chilled, then it's ready to serve.