Season the cooked sushi rice by gently folding in the rice vinegar until well combined, then allow it to cool to room temperature.
Slice the chilled sushi-grade salmon into long, uniform strips approximately half an inch thick.
Peel and slice the avocado into thin wedges and julienne the cucumber into crisp matchsticks.
Place the nori sheets, shiny side down, on a bamboo rolling mat and spread the rice in a thin, even layer over the bottom two-thirds of each sheet.
Arrange the salmon strips, avocado wedges, and cucumber matchsticks in a horizontal line across the center of the rice.
Using the bamboo mat, firmly roll the nori from the bottom up, applying gentle pressure to create tight cylinders, and seal the top edges with a small amount of water.
Use a very sharp, damp knife to slice each roll into eight even pieces, cleaning the blade between cuts to ensure a clean finish.
Arrange the rolls on a plate, sprinkle with black sesame seeds, and serve alongside tamari, wasabi, and pickled ginger.