Rinse and cook the rice. Place the sushi rice in a bowl and rinse under cold water, swishing with your hand, until the water runs mostly clear.
Drain well. Cook according to your rice cooker instructions or on the stove using 1 3/4 cups water per 1 1/2 cups rice. Let it rest 10 minutes after cooking.
Season the rice. Warm the rice vinegar, sugar, and salt in a small pan or microwave until dissolved.
Transfer hot rice to a wide bowl (a wooden bowl is ideal), drizzle the vinegar mixture over, and gently fold with a spatula to coat. Fan to cool to room temperature. The rice should be slightly sticky, not wet.
Prep the fillings. Slice the tuna into long, even strips about 1/2 inch thick.
Slice the avocado lengthwise into thin slices. If you like, toss the tuna with a few drops of lemon or yuzu and a pinch of salt for brightness.
Set up your station. Lay out a bamboo sushi mat wrapped in plastic wrap, a bowl of cold water for wetting your fingers, a sharp knife, and your nori sheets. Keep everything within arm’s reach.
Place the nori. Put one sheet of nori shiny side down on the mat with the lines running horizontally.
If your nori is large, you can trim an inch off the top edge for tighter rolls.
Add the rice. Wet your fingertips to prevent sticking. Spread a thin, even layer of rice over about two-thirds of the nori, leaving a 1-inch border at the top. Don’t pack it down—light pressure keeps the roll tender.
Add fillings. Arrange tuna strips in a line along the center of the rice.
Add 2–3 slices of avocado beside or on top of the tuna. Sprinkle with sesame seeds and green onion if using.
Roll it up. Lift the edge of the mat closest to you and fold it over the filling, tucking the nori under to form a tight cylinder. Pull the mat back slightly, then continue rolling until you reach the top border.
Use a little water on the bare edge of nori to seal.
Shape and set. Use the mat to gently compress the roll, shaping it into a neat cylinder. Let it rest seam-side down for a minute to set the seal.
Slice cleanly. With a very sharp knife, slice the roll in half, then cut each half into 3–4 pieces. Wipe the blade with a damp towel between cuts for clean edges.
Serve. Arrange on a plate and serve with soy sauce, wasabi, and pickled ginger.
A light sprinkle of sesame seeds adds a finishing touch.