Start by rinsing the sushi rice under cold water until the water runs clear to remove excess starch. In a medium saucepan, combine the rinsed rice with 2 cups of water and 1 teaspoon of salt, bringing it to a boil over medium heat. Once boiling, reduce heat to low, cover, and simmer for about 18-20 minutes or until all water is absorbed and rice is tender.
Once cooked, remove the saucepan from heat and let it sit covered for an additional 10 minutes to steam further. In a small bowl, mix together 3 tablespoons of rice vinegar, 1 tablespoon of granulated sugar, and 1 teaspoon of toasted sesame oil until well combined. Gently fold this seasoning mixture into the warm rice while fanning it to cool down slightly.
While the rice cools, slice your sushi-grade salmon into bite-sized pieces suitable for topping your crispy bites later on. In a separate bowl, whisk together 3 tablespoons of Kewpie mayonnaise, 1 teaspoon of yuzu kosho, 1 teaspoon of yuzu juice, and 1 tablespoon of soy sauce until smooth and creamy.
Using a large frying pan or skillet over medium-high heat, add enough oil to shallow fry portions of seasoned sushi rice formed into squares or rectangles until golden brown and crispy on both sides—about 3-4 minutes per side should suffice.
Place your crispy rice pieces on a serving platter once cooked; top each piece with a generous dollop of your salmon mixture followed by slices of cucumber and a sprinkle of toasted sesame seeds and chopped green onions for garnish.