Rinse the sushi rice under cold water until the water runs clear. This helps remove excess starch.
In a medium saucepan, combine the rinsed sushi rice and water. Bring to a boil over medium heat, then reduce the heat to low, cover, and simmer for about 20 minutes, or until the rice is tender and water is absorbed.
While the rice is cooking, in a small bowl, mix the rice vinegar, sugar, and salt until dissolved. Once the rice is done, remove it from the heat and let it cool slightly.
Transfer the warm rice to a large mixing bowl and gently fold in the vinegar mixture until evenly combined. Allow the rice to cool to room temperature.
Prepare your work surface by placing a bamboo sushi mat or a clean, flat cutting board. Lay a sheet of nori on the mat, shiny side down.
With wet hands, take a handful of sushi rice (about a cup) and spread it evenly over the nori, leaving about 1 inch of space at the top.
Arrange the rainbow veggies (cucumber, carrot, bell peppers, avocado, and cabbage) in a line across the rice at the bottom of the nori sheet.
Using the sushi mat, carefully lift the edge closest to you and begin rolling tightly towards the top, tucking in the filling as you go. Continue to roll until you reach the empty edge of the nori.
Wet the edge of the nori with a little water to seal the roll. Finely slice the sushi roll into bite-sized pieces, about 1 inch thick.
Repeat the process with the remaining nori sheets and ingredients.
Arrange the sushi rolls on a serving platter, sprinkle with sesame seeds, and serve with soy sauce, pickled ginger, and wasabi on the side.
Notes
Use fresh vegetables for the best flavor and texture.