Begin by preparing your sushi rice; once cooked and still warm, gently fold in the rice vinegar and let it cool completely to room temperature.
Slice the sushi-grade salmon into long, thin strips and ensure the cooked shrimp are peeled and deveined.
Peel the avocado and slice into thin wedges, and julienne the cucumber into matchstick-sized pieces.
Place one nori sheet on a bamboo rolling mat (makisu) with the rough side facing up.
Wet your hands slightly and spread half of the rice evenly over the nori, leaving a one-inch border at the top edge.
Arrange half of the salmon, shrimp, avocado, and cucumber in a horizontal line across the center of the rice.
Using the bamboo mat, roll the nori tightly over the filling, applying gentle pressure to create a firm cylinder.
Dab a small amount of water along the top border of the nori to seal the roll shut.
Repeat the process for the second roll, then use a very sharp, wet knife to slice each roll into eight even pieces.
Serve the fresh rolls immediately with wasabi paste, tamari, and pickled ginger on the side.