Prepare the sushi rice by folding in the rice vinegar and a pinch of sea salt while it is still warm, then let it cool completely.
Slice the sushi-grade tuna into long, thin strips approximately half an inch thick, ensuring you use a very sharp knife for clean cuts.
Julienne the cucumber and green onions into thin matchsticks and slice the avocado into slim wedges.
Place a nori sheet shiny-side down on a bamboo rolling mat and spread half of the rice evenly over the bottom two-thirds of the sheet.
Layer half of the tuna, cucumber, avocado, and green onions across the center of the rice.
Lift the edge of the mat and roll tightly away from you, using a dab of water to seal the edge of the nori.
Whisk together the tamari, sesame oil, and grated ginger in a small bowl to create the zesty dipping sauce.
Slice each roll into 8 pieces using a damp knife and serve immediately with the prepared sauce.