Place the cooked sushi rice in a small bowl and gently fold in the rice vinegar until well combined.
Julienne the cucumber, carrot, and avocado into thin, uniform matchsticks.
Slice the sashimi-grade tuna and smoked salmon into long, thin strips, and ensure the shrimp is cooked, peeled, and deveined.
Lay one sheet of nori on a bamboo rolling mat, shiny side down.
Wet your fingers slightly and spread half of the rice evenly over the nori, leaving a 1-inch border at the top.
Arrange half of the shrimp, tuna, salmon, and vegetables in a horizontal line across the center of the rice.
Using the mat, lift the bottom edge of the nori and roll it tightly over the fillings, pressing firmly as you go.
Repeat the process with the second nori sheet and remaining ingredients.
Use a very sharp, damp knife to slice each roll into 6 to 8 pieces.
Serve immediately with tamari for dipping.