First, place the sushi rice in a fine-mesh sieve and rinse it under cold running water. Continue until the water runs clear. This step is crucial for removing excess starch. Next, combine the rinsed rice and water in a saucepan, bring it to a boil, then cover, reduce the heat to low, and let it simmer for about 18-20 minutes until the water is fully absorbed.

While the rice cools slightly, prepare the seasoning. In a small saucepan, gently heat the rice vinegar, sugar, and salt over low heat just until the sugar and salt have completely dissolved. Pour this warm vinegar mixture over the cooked rice and use a rice paddle or spatula to gently fold it in, being careful not to mash the grains. Let it cool to room temperature.

Place a bamboo sushi mat on a flat surface, covering it with plastic wrap to prevent sticking. Lay one sheet of nori on the mat with the shiny side facing down. Wet your hands in a bowl of water, then take a handful of sushi rice and spread it evenly over the nori, leaving about a one-inch border at the top edge.

Arrange a few strips of cucumber and slices of avocado in a horizontal line across the center of the rice. Using the bamboo mat as a guide, lift the edge of the nori closest to you and begin rolling it tightly over the fillings. Apply gentle, even pressure as you roll to create a firm cylinder.

To seal the roll, lightly dampen the one-inch border of nori at the top with a little water and press it to close. Use a very sharp, wet knife to slice the roll into 6-8 uniform pieces. Wiping the blade with a damp cloth between each cut will ensure clean, beautiful slices.