Rinse the sushi rice under cold water until the water runs clear. Cook the rice according to package instructions.
In a small saucepan, combine rice vinegar, sugar, and salt. Heat over low heat until the sugar dissolves. Remove from heat.
Transfer the cooked rice to a large bowl and stir in the vinegar mixture. Let the rice cool to room temperature.
In a small bowl, mix mayonnaise and Sriracha sauce. Add the cooked shrimp to the bowl and toss to coat.
To assemble the sushi stacks, place a round cookie cutter on a plate. Add a layer of rice at the bottom, followed by a layer of avocado, a layer of spicy shrimp, and a sprinkle of green onions and sesame seeds.
Carefully lift the cookie cutter to reveal the sushi stack. Repeat to make additional stacks.
Garnish each stack with pieces of Nori seaweed.
Serve the spicy shrimp sushi stacks immediately and enjoy!