1 Place the sushi rice in a sieve and rinse with cold water unti the water runs clear. Drain in a colander for about 20 minutes. Place rice and 500 ml (approximately 2 cups) of water in a pot and bring to a boil.
2 Cook uncovered for 2 minutes, then cover and cook until rice is tender and absorbed almost all liquid, about 20 minutes. Remove pot from heat, remove lid and cover with a kitchen towel. Let stand for 10 minutes.
3 In a small pot, bring 3 tablespoons rice vinegar, 1 tablespoon mirin, 2 teaspoon sugar and 1 teaspoon salt to a simmer, stirring until sugar and salt have dissolved. Place the rice in a bowl and fluff with a fork to cool quickly. Add the vinegar mixture to the rice and let cool completely, about 30 minutes.
4 Rinse cucumber, wipe dry and cut into very thin slices. In a bowl, mix cucumber with a pinch each of salt and sugar, the remaining vinegar and sesame oil. Let marinate for 15 minutes.
5 Whisk together eggs, soy sauce and mineral water in a bowl until frothy.
6 Rinse cilantro, shake dry and pluck leaves.
7 Heat 1 teaspoon oil in a non-stick pan. Pour half of the egg mixture into the pan and allow to cook until omelet is set.
8 Sprinkle the omelet with half the cilantro. Roll up the omelet firmly and let cool on a plate. Repeat with remaining oil, egg and cilantro to make a second rolled omelet. Cut the cooled omelets into pieces, about 2 cm (approximately 3/4 inch) thick.
9 Peel the shrimp, leaving tail intact. With a small sharp knife, cut a slit along the back of the shrimp and devein. Rinse shrimp and pat dry.
10 Fill the pan with about 2 cm (approximately 3/4 inch) water. Season with salt and add remaining mirin. Bring to a boil, add shrimp and cook for 2 minutes.
11 Remove shrimp with a slotted spoon and plunge them into a bowl of ice water to cool. Drain well.
12 Toast sesame seeds in a small dry pan. Use kitchen shears to cut the seaweed sheets into very thin strips.