Place the rice in a fine mesh strainer and rinse until the water that runs out of the bottom is clear. This removes some of the starch from the rice. In a medium saucepan, combine the rice and 2¼ cups (532g) of water.
Bring to a boil, then cover and reduce the heat to low. Cook until the rice is tender and the water has been absorbed, about 20 minutes.
In a small bowl, whisk together the rice vinegar, sugar and salt. Remove from the heat, sprinkle with the rice vinegar mixture, and fluff the rice with a fork and let cool.
Line a quarter sheet pan (9”x13” / 22cm x 32cm) with plastic wrap, then spread the sushi rice evenly, pressing it down so that it is tightly packed about ½”-thick (1.3cm). Transfer to the refrigerator for at least an hour, and up to overnight.
Lift the plastic wrap from the pan, then use a knife to cut it into 12 even squares or use a 2” (5cm) circle cookie cutter to cut out circles.
Heat the vegetable oil in a skillet to 375°F (190ºC). Fry only a few pieces of rice at a time in the pan. Cook the rice undisturbed until one side is golden brown and crispy, about 2 minutes. Flip and continue to cook until deeply golden brown and crispy all over, about an additional 2 to 3 minutes.
In a small mixing bowl mash the avocado until smooth then add the lemon juice and season with salt.
Remove from the pan to a paper towel-lined plate or a cooling rack set over a paper towel-lined baking sheet to drain. If cooking squares, cut each square of crispy rice in half.
Spoon the avocado puree over the crispy rice or add to a piping bag to pipe it onto the rice. Top with the salmon slices then garnish with sesame seeds and serve immediately.
Notes
Pro tip: Press harder than you think you need to. The rice block needs to be dense and compact to hold together during frying.