Mix the cooked sushi rice with the rice vinegar in a small glass bowl until well combined.
Slice the sushi-grade salmon and the avocado into thin, uniform strips.
Place one nori sheet on a bamboo rolling mat and spread half of the rice across it, leaving a one-inch border at the top edge.
Arrange the salmon strips, half of the cucumber, and half of the avocado in a horizontal line across the center of the rice.
Roll the bamboo mat away from you, pressing firmly to create a tight, even cylinder.
Repeat the process with the second nori sheet, using the cooked shrimp and the remaining cucumber and avocado.
Use a very sharp, damp knife to slice each roll into eight even pieces to prevent tearing the seaweed.
Serve the rolls immediately with tamari, wasabi paste, and pickled ginger on the side.