Slice the sushi-grade ahi tuna into long, thin strips approximately 1/2 inch thick.
Julienne the cucumber into thin matchsticks and slice the avocado into thin wedges.
Lay one nori sheet on a bamboo rolling mat, shiny side down, and spread half of the cooked sushi rice evenly over the bottom two-thirds of the sheet.
Drizzle a small amount of rice vinegar and sesame oil over the rice for seasoning.
Place half of the tuna strips, cucumber matchsticks, and avocado wedges in a horizontal line across the center of the rice.
Using the bamboo mat, tightly roll the nori from the bottom up, tucking the ingredients in as you go, and seal the edge with a drop of water.
Repeat the process for the second roll, then use a very sharp, damp knife to slice each roll into 6-8 even pieces.
Serve immediately with tamari, pickled ginger, and wasabi paste for a clean and zesty meal.