Place one nori sheet on top of a piece of parchment paper with the shiny side facing downward.
Divide the seasoned sushi rice into four equal portions. Spread one portion evenly over the nori sheet, leaving about a 1-inch border uncovered along the top edge to help seal the roll.
Arrange several strips of ahi tuna across the center of the rice, then add slices of avocado and cucumber in a neat line to create an even filling from end to end.
Starting from the edge closest to you, lift the parchment paper together with the nori and gently fold it over the filling. Press firmly but carefully to create a compact roll. Continue rolling forward while pulling the parchment paper away as you go so it doesn't become wrapped inside the sushi. Roll until the exposed edge of the nori seals the roll completely.
Leave the finished roll wrapped loosely in the parchment paper for 2 to 3 minutes. This brief resting period helps the nori soften slightly and allows the roll to hold its shape. Repeat the same process with the remaining rice, nori sheets, and fillings.
Remove the parchment paper and place each sushi roll on a cutting board. Using a very sharp knife, slice the roll into 1-inch-thick pieces, wiping the blade clean between cuts if needed for neat, clean slices.
Arrange the sushi rolls on a serving platter and serve immediately with soy sauce, wasabi, or sriracha mayo for dipping. Enjoy as a light meal, appetizer, or homemade sushi night favorite.