Place the cooked sushi rice in a small bowl and gently fold in the rice vinegar until well combined.
Slice the sushi-grade salmon into long, thin strips approximately half an inch thick.
Lay one sheet of nori on a bamboo rolling mat, shiny side down.
Wet your fingers slightly and spread half of the seasoned rice evenly over the nori, leaving a one-inch border at the top edge.
Arrange half of the salmon strips, half of the julienned cucumber, and half of the avocado slices in a horizontal line across the center of the rice.
Using the bamboo mat, firmly roll the nori from the bottom up, tucking the ingredients in tightly as you go.
Repeat the process with the second sheet of nori, using the cooked shrimp as the primary protein along with the remaining cucumber and avocado.
Use a very sharp knife dipped in water to slice each roll into 6 to 8 even pieces.
Arrange the sushi pieces on a platter and serve immediately with tamari, pickled ginger, and wasabi paste.