Step 1: Prepare the Rice
Rinse the sushi rice several times until the water runs clear. Cook the rice with the water according to your rice cooker's instructions or prepare it on the stovetop.
Step 2: Season the Rice
In a small bowl, whisk together the salt, rice vinegar, sugar, and toasted sesame oil until the sugar dissolves completely. Fold the mixture gently into the freshly cooked rice until evenly coated.
Step 3: Chill the Rice
Line a square baking dish or container with plastic wrap. Press the seasoned rice into an even layer about ½ inch thick. Cover tightly and refrigerate for at least 3 hours, or overnight, until firm.
Step 4: Cut the Rice
Remove the chilled rice from the container and slice it into bite-sized rectangles or squares. Pat each piece dry with paper towels if any moisture has formed.
Step 5: Fry Until Crispy
Heat about ¼ to ½ inch of vegetable oil in a skillet over medium-high heat. Once hot, carefully add the rice pieces, leaving space between each one. Fry for about 2 minutes per side, or until both sides are crisp and golden brown. Transfer to a wire rack to drain excess oil.
Step 6: Prepare the Salmon
In a medium bowl, combine the diced sushi-grade salmon, Kewpie mayonnaise, yuzu kosho, yuzu juice, soy sauce, and sesame oil. Mix gently until evenly coated.
Step 7: Assemble
Place a slice of cucumber on top of each crispy rice piece if desired. Spoon the salmon mixture over each rice square.
Step 8: Garnish and Serve
Finish with toasted sesame seeds and chopped green onions. Serve immediately while the rice is still warm and crispy.