How to Make It
Put the rice in a medium saucepan, rinse well and drain. Add the water and bring to a boil. Cover and cook the rice over low heat for 12 minutes. Remove from the heat and let the rice stand, covered, for 10 minutes.
In a small bowl, stir the vinegar with the sugar and 3/4 teaspoon of salt until dissolved. Spread the hot rice on a large rimmed baking sheet in an even layer. Sprinkle the vinegar mixture evenly over the rice. With a wooden spoon or a pastry scraper in one hand and a simple paper fan in the other, lightly stir and toss the rice while fanning it until the rice is glossy and cool.
In a small dry skillet, cook the sesame seeds over moderately high heat until toasted, about 1 minute. In a small bowl, mix together the wasabi powder and hot water to make a paste; keep covered.
In a medium saucepan, heat 1/2 inch of oil to 325°. With a long, sharp knife, cut the skin from the salmon fillets, leaving 1/4 inch of flesh on the skin. Season the salmon skin with salt and pepper and dust with flour. Fry one at a time over moderately high heat, turning once, until browned and crisp, about 3 minutes. Drain the salmon skin on paper towels and repeat with the rest.
Put a nori sheet on a bamboo sushi mat, shiny side down. With moist hands, pat 3/4 cup of the rice on the nori in an even layer, leaving a 1-inch border all around. Sprinkle 1/2 teaspoon of the toasted sesame seeds over the rice, then spread 1/4 teaspoon of the wasabi paste in a thin line across the rice. Lay a salmon skin on the rice nearest you and top with one fourth of the cucumber strips. Lift the end of the bamboo mat nearest you up and over, pressing to tuck the skin and cucumber into a cylinder. Tightly roll up the fillings in the rice and nori. Repeat to form the remaining 3 rolls. Cut each roll into 6 pieces and transfer to a platter. Serve with a small bowl of soy sauce and extra wasabi, if desired.